Remove battery - take to shop that can perform LOAD test.Replace if defective. LOAD test replacement battery.

While battery is removed, take a piece of sandpaper - take apart and clean all start circuit connections (including battery terms)to bright metal. replace any heavy leads that are badly corroded or damaged.
Put known good battery back in machine. Retest
Repost if further problems..

Leaving the key on overnight is not going to affect the starter. The starter only has current to it when the key is in the START position.
As too the starter being "hot to touch". A starter will heat up very rapidly when it is engaged for a long time (more than a few seconds is a long time to a starter). Having a low voltage condition (weak battery) will exaggerate the heating of the starter even though the starter is producing much less output power (actual cranking speed).

I did try a battery that was known to be good - same results, very sluggish, when it even did attempt to crank.

I will try cleaning the terminals and see what happens.

Before this stalling/won't-crank situation yesterday, I took no exception to the way the tractor was operating.

Weird to have two new problems crop up simultaneously.

the only thing about that kohler engine is it is particular about wanting an OEM fuel filter - has to do with the filtration level (no aftermarkets) and that the filter be installed in the correct direction.
The fuel filter appearing to be partially empty is just a phenomenon - mownie knows how to explain such....

The way the engine sputtered to a halt may be due to the battery and system voltage falling below the threshold at which the fuel solenoid valve on the carburetor will operate at.
If there is a fuel solenoid located on the carb, the stalling might simply be due to low voltage.

Posting the Sears 917.xxxxxx number would allow one to look at the proper schematic and "possibly" spot something else. Also it would tell us exactly WHICH Kohler you have. (probably an SV-600?)
If not, it would still give us an the knowledge to tell you how to troubleshoot the charging system.

Bill, The model is 917.275660, with the 20HP SV600 engine.

Mowie, there is a cylindrical device at the bottom of the bowl on the carb, with a single red wire running to it.

rcbe6, the filter is a B&S, (I know, shouldn't have done it) but it's been on there for 30 hours since early summer with no issues.

I have a spare (new) voltage regulator that I swapped out just for kicks, made no difference.

I cleaned all the battery cable terminal lugs, pulled the connector from the ignition switch (terminals looked bright and clean) put a jump on the battery one more time, which made it attempt to crank with a bit more ooomph, but still not enough to make her start.

Under what conditions would the starter be the suspect?

Did you get the battery load tested ?

Carb solenoid and a different Voltage Regulator will have nothing to do with cranking.

Have you pulled the spark plugs to make sure the cylinders aren't hydrolocked?
Unlikely, but it's a FREE thing to test.

Charge the battery and get it load tested. Most auto parts stores can do the load test.

The engine has to run to test the charging system. To run, it has to crank to start.

IF you get the battery charged, you can probably do a simple load test in situ.

Turn on the headlights.
IF the engine cranks, the battery is probably "adequate".
IF it doesn't, and the headlights dim to nothing, it's probably "toast".

Once a battery is 2 years old, it's suspect in L&G equipment.

rcbe6 - Unable to get the battery load tested this afternoon, will attempt to get it done Friday. Also, I tried another battery, with same results - wouldn't crank enough to start.

bill - I will check for hydrolock tomorrow. The battery is only three months old, not that it couldn't be defective this soon.

Gents - One other thing, FWIW, if anything - the ammeter needle goes only a little bit to the minus side of "0" when attempting to crank.

That's just the carb & starter SOLENOID draw.
The crank circuit doesn't go through the ammeter, since it can draw a couple hundred amps.

OP - when you get to where you try to test the starter again, have an assistant to CAREFULLY look to see if if your deck drive is moving while the engine is cranking. Long shot, I know.. but if your PTO clutch is seized up, the extra drag from the starter also having to drive the deck could be part of the problem.

rcbe 6 -

I'll check for that PTO seizure in the morning. That's a interesting possibility. Something is definitely creating a heavy drag when attempting to start.

I charged the battery overnight, then cranked the engine without the spark plug in, it cranked and spun very freely. When I reinstalled the plug, cranking effort changed to very, very sluggish, barely at all. Maybe it is trying to drive everything at once?

Also, I found five of the 10mm head bolts that run just below the the flywheel had apparently vibrated loose, one to the point that it was standing high enough to contact the underside of the flywheel, so I retightened them.

Will advise what I find.

quote: Also, I found five of the 10mm head bolts that run just below the the flywheel had apparently vibrated loose, one to the point that it was standing high enough to contact the underside of the flywheel, so I retightened them.Unquote.

that raises the possibility of a sheared crankshaft key - may hafta pursue that after resolving battery question.

rcbe 6

Disengaged belt from PTO clutch - no difference in cranking effort (or lack thereof), still poor.

May venture down to local mower repair shop..........

Remove the valve cover and have a look. Rocker studs can back out on these just like an Intek.

Well, I wish I'd seen tomplum's post earlier.

I got the machine back today from the local mower shop. The rocker studs had backed out and the push rods were bent. When the guy opened it up he said a valve was hanging out. The good news is the studs hadn't chewed up the block threads on their way out.

Parts (2 each - rocker posts, retainers, studs, rocker arms, push rods, 1 v/c gasket) were $56, labor $95, but at least now it's up and running again, and that feels good....