Look on the rear of the deck for a plate with model and serial number on it. Could also be on bottom (backside) of handle.
Depending on model, there is a lever on top of carb for light and heavy cutting. Check it's position. Also there is an air vane on top rear of carb that sticks up through an opening in the air baffle under the shroud. It could be binding or have a broken spring. Get a new air filter. You will ruin the engine running without one.
Repost if you find model number.

Did a little more googling...(The mower is in the next county, at the camp, unfortunately)...
It's a 5126, with the F380.
Like this one (but in better shape):
http://i78.photobucket.com/albums/j93/my_crib_too/1%20Non-Commercial/5126.jpg

The air vane mentioned by whizzer acts as the governor, does it?

The lever's okay, up until a few mowings ago, I could cut most of the lawn on the slow speed, and bump it up for the heavier parts. The lever works and the speed goes up and down, but the speed overall is way to slow, and excessive smoke.

The foam element looks like new, but the issue goes away completely when I remove it. (No, I won't use it with no filter element...I just cut a strip or two as a test)

Pull the filter again and look into the air intake (engine off). The throttle plate should be wide open (edge to you). Take a stick and push the air vane over and release to see if it snaps back to wide-open. That means its basically working but the governor may be out of adjustment.
Excess smoke on a 2-cycle is always too much oil being burned. This could be from too much oil in the fuel or too much fuel mix being burned.
On an old LB like that, I would want to see that the crank seals are good and that the exhaust ports and muffler are not clogged with carbon.
A new filter element would seem to be a good investment - yours would seem to be clogged up.
A 2-cycle speeds up as it runs out of gas because the mixture leans out.
Changes in running associated with changes in mower attitude/direction usually point to a stuck of failing carburetor float. Pick up the back of the mower and drop it from 6" and try it. Sometimes it will jar the float loose. Even if it does it again, this would indicate you probably need to put a float in it.
Governor operation: the fan made into the flywheel blows on the air vane, trying to close the throttle. Spring tension is adjustable to set the desired RPM. The throttle mechanism acts as a pre-set and does not have direct control of the throttle plate - it moves a slider on top of the air box which tensions or relaxes the governor spring - the end of the spring is attached to the slider. At the base of the air vane these is a knurled disc which allows a small RPM adjustment. It should click when turned, and four clicks is about the limit. Clockwise should tighten the governor spring, resulting in higher speed.
That is, assuming this engine is set up like other LBs.
Last thought; is there a needle valve for adjusting the mixture? You might need only a new filter element and a slightly leaner mixture.

https://lookup3.toro.com/ttcGateway/acrobat/manuals/lball.html

This is the manual Lawnboy shows for your mower.
Might help you fix problem.

All great info...thanks so much.

I'm not sure if I'll get down to the camp with the storm coming this weekend but I might take a quick run down and bring the LB back with the propane lanterns and stove (in case we lose power here). If so, I'll see what I can sort out.

Thanks again!

Well, I had a few minutes to check a few things over last night. Gotta love these things, engine shroud off, removed carb, float bowl....tools used, 1 screwdriver.. :-)

So..float bowl was clean and crud-free, so signs of gunk in the needle valve, moves freely, etc. Cork float is all in one piece, and once the surface gas dried upp it doesn't seem saturated.

The air vane moves freely, spring not broken. Throttle is held wide open, vane will close throttle, spring back to wide open, seems fine.

I blew through the ports I could with the carb off....did NOT touch mixture screw (I assume it's the brass one sticking straight up behind the throttle through-shaft?) The mixture screw has not been touched at all (as long as I've had the mower, and it worked well since I've had it).

Exhaust port is clear.

Pulled the plug out, cleaned it up, a fair amount of wet sludge (from running so rich)..cleaned it up like new, reinstalled.

So, that all checks out.....put everything back together, same issue.

It's running rich to the point that you can tell it's sputtering when you move the air vane...it should rev up but it sputters instead, like it's way too rich.
It ran a few minutes while I tried each direction on the click wheel (it changes the idle speed but it remains rich and doesn't want to rev up...sputters instead), and it left a big oily spot on the lawn under the exhaust port....so..yeah, rich...

Also, it's spitting gas out the intake. Not a huge amount, but enough that it gets the air filter wet, and will fire drops into your eyes if you stick your head down there with the air filter off. LOL

I didn't fiddle with the mixture screw. (Any time I fiddled with carb mixtures in the past ended with a trip to the small engine shop to have them fix what I screwed up.)
If someone can confirm how many turns from bottom it should be, I'll pull it out in case there's a piece of dirt or something in it...
As for the adjustment..it 'should' be good..it was never changed...

So...recapping::: rich, will idle not too bad, but as soon as you cut any grass it just slows right down and stalls. Will not rev up any significant amount when moving the air vane..it wants to but just loads up with fuel and sputters instead.

The issue came on slowly over 2-3 mowing sessions..it wasn't there all of a sudden...it came on slowly and got worse and worse over time.

Feel free to toss the hints at me....thanks in advance!!

Did you try a new air filter?
If it runs well without filter that's the first thing to do.
Also, seems I read somewhere that an air filter wet with fuel mixture when engine is not flooding is a symptom of leaking reed valves.

I didn't try a new air filter because now it's progressed to the point that it runs almost as bad without the air filter....

I didn't try a new air filter because now it's progressed to the point that it runs almost as bad without the air filter....

It does sound like a reed problem, and they do come on slowly. Fuel should never shoot back into the filter when the reed is sealing properly. With a good reed there is only a barely visible "fuel fog" on the carburetor side of the reed when the engine is running.Also, the only way to test a cork float is to put it in a container of fuel and see if it is buoyant (floats high on the surface).

No experience at all with 2-strokes, so kind of learning as I go...

But yeah, you can see the big drops of fuel flying out and landing on the mower deck.

I'll float the float and see what it looks like...I had it off and it didn't 'feel' heavy...but obviously that's just guessing.

I'll pop the carb off again and check the reeds...When they 'go', are they visibly cracked or anything? I had a look at them when the carb was off the other day but it was more curiosity than an inspection, since I was sure I had a carb problem... (and it very well may be a carb problem..we'll see)

Every 2-cycle I've had would shoot a little fuel back out of the carb throat. This is because there is a small interval between the piston starting to move down and the closing of the reed valve. I think the problem here is simply excess fuel in the carb throat for whatever reason, which gets expelled during the normal operation of the reed valve. Bad reed valves do not cause a rich condition - rather the opposite, as they no longer seal, preventing the needed pressure build-up in the crankcase and reducing the volume of the intake charge, which includes air and fuel, so less of both would make it into the combustion chamber.
Fuel metering in this engine is out of whack, whether from a bad float or some other problem, like a maladjustment of the needle valve (if so equipped).