I would seek local professional help, before trashing that engine! There are lots of things that i have seen novices do when working on their engines, that are fixable without full engine replacement.
One such fellow brought his mower in-said it wouldn't start, but he had "topped off" the engine oil, but it wouldn't turn! I found he had poured in the oil, to the top of the dip-stick tube, which act filled the whole block and all of the passages. He had wondered to me why it took so much more oil, when he only drained out so much less!
I showed him the marks on the dip-stick! Oh, sez he---i wondered about those marks, but didn't know why they were on the stick! WOO-HOO!! by: Rusty Jones

I had a couple neighbors look at it, one of whom had been a car mechanic a few years back. The consensus seemed to be that since the flywheel will not rock or turn at all and removing the spark plug did not cause any oil to leak out, that the motor is seized.
Without a way to transport it, I'm looking at $100 bucks for Sears to make a house call. I suppose I could buy a flywheel removal tool and try to take that off manually and make it move. But, I've heard horror stories of engines breaking down again after being un-seized that way.

I firmly believe that you would be much further ahead, to hire somebody to cut yer grass, and leave the engine work to somebody more experienced than what you sound like!
Yes, you could invest $900 in another engine, but then what--it'd be installed in an old machine, and you would probably have more troubles with the transmission!
I do a lot of service work on Craftsman mowers/tractors, and from what i have seen, they seem to hold up well.
Oh, yes, there are some out there, who are stuck on JD, Troy-bilt, Big Boy, and other high-priced lawn machines, but i have several used Craftsman tractors i use for my own property, and with proper care-they are just as good as those higher priced machines. And, cost much less to repair!

Don't get me wrong. I've loved my Craftsman. Which is why I'd consider having the engine replaced. I've owned it for five years and never really had much trouble. I've performed seasonal maintenance as recommended, cleaned and replaced blades, cleaned the carburetor once, all with little or no hassle. As I mentioned, the last oil change coincided with something going awry and the engine locking up. Five years of mowing with this tractor has probably already paid for itself in terms of what would be needed to cover the costs of a lawn care company.

I'd like to hear from someone more knowledgeable than I, which there a probably a lot of here, if the engine in my original post (331877-3036-G5) would be a compatible replacement for the factory motor.

Rustyj, it sounds like in your experience, new engines on Craftsman mowers typically lead to other issues that make engine replacement a less than desirable option. Is that correct?

Well, if i had a 1995 Buick, and the engine went bad, would i install a brand new or rebuilt engine? Especially since by now, here in salt country, the body is holed in spots, akin to a worn mower deck?
No, unless it had never been driven in salt!
If your mower hasn't been run hard and put away wet, yes, ya might do well to replace the engine/ short block. I've done that and gotten many more years of use from a good old lawn tractor. But, its up to you.
The way i feel--once ya lay yer money down and buy a new machine, ya might just as well replace the engine, and keep what ya got. Altho, if ya worry about what the neighbors say, then buy new! I don't, and my oldest machine is a 1983 SNapper Rear engine rider. The Toro/Wheel Horse may be even older! Don't know about the old gray Craftsman. They all run well! And if the engine goes "BANG" it gets a good used one installed. To Heck with the neighbors! Rustyj

I can tell you this much.......you should not try to do the work yourself in regard to attempting to FIX the locked engine.
Your statements about taking off the flywheel pretty much bears out that you lack the skills to go inside an engine.
It isn't the flywheel that won't move here.........it is the crankshaft that the flywheel is attached to that is seized.
Prudence says that your money will be better spent hiring out the work.

There are several things here. First, an engine does not seize from nearly changing the oil, something is being left out. The IPL for the engine shows a Slinger which would be responsible for the bulk of the lubrication even though the engine has an oil filter and oil pump.

Also, just recently, a 48" Simplicity hydrostatic drive Lawn Tractor with a B&S 22 hp V Twin engine was given away because the "engine was seized". The person receiving the tractor sold it for $50 also thinking the engine was seized. This second person is a very experienced tech. Turned out the starter gear was jammed in the ring gear.

I had one that was "seized". Flywheel magnets had come loose locking the FLYWHEEL.

But to the OP's original question, yes, the 33 series engine will replace the 31 with no problem EXCEPT the charging system MAY have to be switched which they will interchange BUT, as said previously, given your aversion to removing the flywheel, it is questionable whether you should undertake any of the switch.

Too bad you don't live close, I have an abundance of good used and rebuilt engines in the range.

Walt Conner

It appears your current engine had the dual circuit alternator and the new engine has the tri circuit alternator.

Normally, you would swap the stator & flywheel to interchange the charging system.

However, I see the new engine uses different part numbers for its flywheel vs "the old standard" part numbers.
Ergo, I'm not sure the new flywheel will fit.

Does not matter whether the flywheel interchanges or not, the stater will and since the dual circuit would have only been producing 3 amps DC, no problem. I would not hesitate to change both if opportunity presented its' self given B&S's very high interchangeability rate. Number difference MAY represent a difference in ring gear which is something that may require changing the starter or starter pinion gear. I did not see any outstandingly difference in the ones I have had.

Walt Conner

As a follow up, the 31 engine has two flywheels listed as options, one of these part numbers matches the 33 engine in questions leaving no doubt the flywheels will interchange.

Walt Conner

Thanks to everyone for the informative responses. Obviously, I am at a novice level when it comes to mower engines so all feedback has been useful and is greatly appreciated.

Now I have to make the tough decision of spending a minimum of $100 on a house call diagnosis (plus labor and parts assuming the motor is able to be saved) or $500-$600 for a new motor (and trying to teach myself to install it with help from friends). Or the 3rd option of at least $1300 for a new tractor.

Might i say this: Since you evidently do not have much experience with lawn tractors and how they operate, and engines that have gone "BANG", it might be better for you to bite the bullet and buy a new machine.
Replacing engines, and all that goes with it, is not for novices. Have you heard the saying: "Pouring sand down a rat-hole"? Thaat is what happens some times when installing a used engine that you may have bought, without hearing it run. And try to keep the oil at the proper level, by checking it frequently, before starting the engine. The double stick method is best, as oil from the previous running will stay high on the dip-stick, and if you just pull out the stick, and don't wipe it off, and stick it again---the oil can be down too far, and the engine can and will go "BANG" from low or no oil! BT/DT! RJ