Before you jump to any conclusions about valves/adjustment, check to see if the fuel tank cap vent hole is plugged. This can result in symptoms similar to what you describe. The only part of your story that is at odds with this is where you said wouldn't restart after sitting for a few days. It may be just coincidental that the spark plug failed (if it did). Try cleaning out the fuel cap vent hole with a piece of stiff wire or an unfolded paper clip. If this was the problem you should know after mowing a short while.

Well, it's not the vent hole. I check it (it was clear), added some gas and put in some seafoam to help remove carbon. When it started missing I slowed down and it went a little while longer but still quit. So I let it sit, then went back to mowing but this time only used 2/3 throttle. It did the rest of the lawn without a problem. Not to fuel the "what throttle setting" debate, I think it kept it cool enough to not trigger the problem. Either that, or the seafoam cleared out the carbon that was causing preignition and causing it to stall. Next time I need to mow I'll try full throttle again and see what happens.

Something was (still is?) going wrong when it got too hot. Maybe too much carbon caused preignition, maybe the valve clearence changed too much. I dunno...

When you have the hot start problem, check the spark. A failing coil can get worse as it heats up. You might first check the spark with a cold engine to have a comparison. (Still got the old plug? Open the gap to about 3/16" and use as a tester)

I'd check/replace the fuel filter. It may be restricted "just enough" to cause the carb to run out of gas on an "extended" heavy load. It's about $4 or so, so if that isn't it, call it "maintenance".

Valve lash is set with the piston 1/4" PAST TDC.
Intake .004"
Exhaust .006
+/- .001"
IF nothing else, you could take a .006" feeler gauge and see if the lash is excessive without "tweaking" anything.

Can the carb fuel adjustment screw be opened a tad,if it has one?tbk

How is valve lash checked? I've done it on car engines but haven't opened up one of these small ones. I'll change the fuel filter too while I'm at it.

This advice from Walt2002 did the trick on my 12HP briggs. THought you could give it a try on yours. My engine was running rich when hot and surging, trying to die. Quote below and good luck.....

"Sounds to me like the engine is running too rich. You do know how to adjust the carb? Screw sticking straight down out of the bottom of the carb float bowl, turn it clockwise a little, if you were looking at the head. Turn it until the engine falters, turn it back counter clockwise until it falters, split the difference. Do the Same at idle with the idle screw on the top of carb.

Walt Conner "

"How is valve lash checked? I've done it on car engines..."
Nothing different except the piston has to be 1/4" ATDC.

"This advice from Walt2002 did the trick on my 12HP briggs."
I don't believe his carb has any such adjustment. At least according to the IPL.

Since you can start your engine without choke, then it misses, then it dies, it's like your engine is always on choke. I suggest that you check your choke operation (cable too short or not returning all the way?). Also, check your air cleaner. A dirty air cleaner acts like a choke. A quick air cleaner test is to take it off in a relatively dust free area (a garage with concrete floor is good) and fire up the engine.

-Deerslayer

I'll check the choke and air cleaner as well. It probably is running rich, but why would it make it hard to crank when hot? I can understand running rough, missing, and blowing black smoke (which it doesn't do), but why would it not crank sometimes when hot?

Sometimes when it stalls and I get it restarted it'll put out a puff of black smoke, but not while it's running.

"but why would it not crank sometimes when hot?"
"If I jump it it cranks much faster and will usually start."

Maybe your tractor battery is weak.

-Deerslayer

Either the model number or the type number is incorrect.
If the model number is correct, then the valves should
be at .005-.007 intake, and .009- .011 exhaust
and the valve cover is behind the carb.
If the model number is not 280707, and it is an overhead
valve, the adjustment will be different.
The first 2 digits of the code number is the year it was
made, and if they are 84 or earlier, the engine may have points but I doubt it. I would pull the head, look at the
valves and piston, knock off the carbon. Pull the carb
and take it apart and clean. And remove the valve cover and
check the gap, you will likely find one is a bit tight.
As the engine gets overheated, the block actually warps back and that makes the gaps close, so you might want to check the fins on the top of the engine for debris and mice nests, and look for chewed up wires too.
Fish

Update: I changed the fuel and air filters. The fuel seemed to flow fine when pulling the old filter, so I don't think that was it. The air filter looked somewhat dirty, but not too awful. When I mowed again I made it through the whole yard stalling 3 times. 1st it was out of gas, so that doesn't really count, but it restarted fine. 2nd was when I was almost done, but it did restart. 3rd was right after I finished and it wouldn't restart, so I just put it away.

Maybe the air filter helped some, but I kinda think the seafoam is clearing out the carbon and helping the most. Maybe it'll keep getting better and won't need to be opened up.

If I pull and clean out the carb what gaskets am I going to need? Same will pulling the valve cover and the head. I'd like to get them before starting the job.

And it is an L-head engine, I guess the type number is wrong.

Thanks for all the help.

Fisher is correct about the valve clearances. I must have transposed a number when looking things up.
I was thinking it was an OHV engine.

What, if any, gaskets will I need if I check the valve clearances? And how are the clearances adjusted?

Thanks.

To check lash, you'll have to remove the breather /valve cover, which means you probably have to remove the carb first to get to the cover.
To adjust (you'll love this part)-you have to remove the valve, which means removing the head.
IF not enough lash, you grind the end of the valve stem.
IF too much lash, you "grind/lap the valve seat.

Gaskets- IT would be good practice to replace the breather and carb mount gaskets, but you MIGHT get by without.
Add a head gasket if you need to "adjust".

Thanks bill. Where should I look to buy gaskets?

Just as an update, I haven't done anything more to the tractor and it mowed fine last time. I even cut shorter than normal and there was clearly more load, but it had no problems. I'm thinking the seafoam cleared out enough carbon to make it work. The valves may be a little off, but it seams to be working good enough for now.