If you think it's too far gone to put more $ in, get a harbor freight 6 1/2HP engine. They bolt right up w/ metric bolts.
Mike

The thought had crossed my mind. They are wicked cheap. However, I'm a sucker for old iron and want to make sure that I've covered all the bases before slapping a chonda on it. It seems sacreligious in a way to slap a plastic engine on an old horse. I guess I may have to get over my nostalgia...

That old engine may have either worn out piston and rings, or the rings may simply be sticking/already stuck.
The time to check for a sloppy fitting piston is when the head is off. You can get a general impression of piston wear by placing a thumb from each hand at the edges of the piston at the east and west sides of the piston (which is the same plane as the con rod pivots in, crankshaft is mounted as north and south).
Push down on one side first and then the other in alternating fashion. If you can feel any appreciable motion, or hear a distinct slap noise as the piston rocks back and forth, the piston along with the rings is likely worn out. Then if you wanted to be certain you would have to remove piston and mike the cylinder and piston.
Engines that have sat unused without proper prep before storage sometimes have piston rings that want to stick or seize up in the ring grooves on the pistons. Rings that get stuck do not inflate properly and seal to the piston ring grooves and the cylinder walls, increasing crankcase blowby.
The air puffing back out the intake might be nothing more than the effects of the Easy Spin camshaft which is engineered to relieve some compression at cranking speeds to aid in turning the engine for starting. At operating RPM the cam spins too fast for much compression to relieve back.

I should have tried the piston rock test when I had it open. Might be worth taking the head back off and testing it.

I'd also wondered about the stuck ring - he did say it sat in his barn forever. Then he had his mechanic friend go all over it last year - I'm not really sure what the guy really did.

The puffing happens when the engine is running. So I'm thinking the compression release would not be functioning then. Or are you saying the engine is running slow enough even with the throttle open that the release isn't disengaged fully?

The Briggs easy spin camshaft compression release is a concept, not a group of parts making up a compression release mechanism. With Briggs easy spin, there is no actual mechanism. The easy spin camshaft essentially is made with a small "high spot" or "blip" on the camshaft base circle (opposite the large high part of the cam called the lobe).
Whenever the tappet is in contact with the base circle of the cam, the valve for that tappet is closed.
During the compression and power stroke, the intake tappet is riding on the base circle. The Briggs easy spin concept places a very small high point on the base circle corresponding to the compression stroke part of the 4 stroke cycle. When the intake tappet contacts this high spot or bump during the compression part of the cycle, the intake valve re-opens slightly letting just a little pressure escape back into the intake port and manifold. This is what causes the slight "puff" back to the carb on these engines. This concept only works because the very slow RPM during cranking operation allows ENOUGH TIME for the decompression to take place.
Once the engine gets running, the high spot passes the tappet too fast for any appreciable decompression to happen. The higher the RPM, the LESS TIME the valve is open for decompression. At higher RPM there is not even enough decompression to slow the inertia of the induction stream entering the engine. It is a compression release system with no additional moving parts, based solely on the principle of Pressure and Time. At a given pressure, a specific volume of gas will flow through an opening in a specific duration of time. If you decrease the duration of time the volume of gas flow will decrease proportionate to the time.
That's why at higher RPM the decompression is negligible.
I wasn't trying to say that the lack of RPM was any way related to a compression release malfunction.
I was simply stating that the spit back you see is normal for these Briggs engines with the easy spin cam.
In an old engine like this one it can be difficult to read a spark plug's color to determine if the air/fuel mix is too rich or too lean because excessive crankcase blowby (in both directions) often puts engine lube oil into the combustion chamber and that makes it hard to know if it is only burning fuel (gasoline) or if it is also burning some oil.
I would not be afraid to remove the spark plug and get the piston coming up on the compression stroke and fill the combustion chamber up with your favorite "rust bust" product and leave it set for a week like that, adding more if it leaks down. This will permit time for the solvent to work its way down through the rings and grooves. Now don't go pouring a whole can of the stuff in there, cause the idea is to just let the stuff find its way down through the rings and cut the carbon and corrosion.
Oil is cheap, so drain the oil and put in fresh after you soak the rings. Fill the fuel tank with fresh fuel and add some Sea Foam gas treatment (solvent) to the fuel.
Then you want to just run the engine. Run it, run it, run it. You may have to run a whole tank of gas through it to see if it is going to improve. If the problem is due to sticky or stuck rings it should show some improvement after a half tank or so of gas has been used.
If it is due to the engine being wore slam out.....the spark plug will likely foul out or at least be sticky/gummy black after the running.
Good luck.

I appreciate that description - I've read about 10 explanations of this compression release concept and yours is the first that clicked. Call me slow, but thank you!

I tore down the carb again last night and re-cleaned it. Figured no harm, and maybe I'd find something. The screwdriver slot on the main nozzle was pretty bunged up, so I decided not to put it back in because I don't think it's coming back out again. Nozzle itself seemed ok and clean, but I'll be optimistic and just get a new one.

While I'm waiting for it to come in, I started a MMO soak on the rings. Of all the claimed benefits, freeing stuck rings seems to be the one that seems to be commonly reported as successful.

Odds are still pretty good this thing may be worn out. But like I said, I'm a sucker for old iron and it's pretty cheap to try these two things before figuring out Plan B.

Yes, I too am a sucker for old iron.......and aluminum too! :^)
I am more motivated by a challenge to "save" something old from going to the scrap yard than I am by the prospect of just replacing the machine. I am thankful that I have the patience, experience, and (hopefully) enough wisdom to get me through some tough spots. I hope the challenges help to keep my old bag of bones and hair out of "the scrap yard" too.

FIgured I'd post an update, since I had some time to play with this over the weekend. Did about a 4 day MMO soak, the first time it took 48 hours to drain, the second was about 12, and the third fill took less than a work day.

Fired it up and it fouled the plug out in about 30 minutes. The second time it ran about 2.5 hours till it was out of gas. Plug was pretty ugly yet. Cleaned the plug up, fired it up again and tried it out. Believe it or not, it actually has some power now!

I used to be able to kill it when I pulled against the handles when it was in gear - now it will pull me around. I also drove it up and down some pretty steep hills - that's about as hard of a workout I can give it till tilling time.

It will slightly puff white smoke, especially going up the hill so it's still got some issues. I've also noticed I've got to run it richer than it would like at full throttle/no load, so that it will run and pull under load. Not sure if that means anything or not.

All in all, things are heading in the right direction and it's a lot better than when I hauled it home. Next project is getting the PTO clutch cleaned/greased - it's not disengaging very well. Google tells me that cleaning and greasing the dogs should (hopefully) solve that.

Yes, things seem to be heading in the right direction.
Don't be reluctant to just fire it up and run for about10 minutes or more at a time simply to heat it up.
Heating and cooling cycles will further help to crack the rust bond from surfaces during heat up and cool down.
The blow by past the rings at cold start up will help purge stuff from the maze of rings and grooves on the piston.
Just be sure to run it to operating temperature before you shut it down.
Starting and running for only a minute or 2 just puts water into the crankcase, you gotta run it long enough for that water to be driven out of the oil by heating the oil up.

Nothing unusual about needing a richer mix overall than it takes to simply attain governed RPM with no load.
And even though you may need to dial in what you think is rich.............you actually are not really pouring that much fuel out of the carb when the engine is not loaded.
Nope, when the engine attains governed RPM, the governor begins to close the throttle plate. The governor will close the throttle plate as far as it can while still keeping the engine RPM at the selected setting (according to what you are calling for with your throttle control position).
Only when loading of the engine threatens to drop the RPM below the governed RPM and the governor opens the throttle plate up does the carb begin to deliver a greater volume of fuel.