Jim: I've got a 782 and had a similar problem with the carb. I am not sure which of the following corrected it, but the thing runs perfect today. However, all the advise I got led to this: 1) Ifa you gotta no spark, ita noa run. Ifa you gotta weak spark, ita run notso good. Thus, first replace the sparkplug wires with COPPER CORE wires - they will make a difference immediately if your wires were funky. Next, set the timing at the RPM called for by the KT17 manual...I think it is WOT (wide open throttle...aka 3600 rpm). Use a timing light (if you got one) or by setting point gap if you dont. If your points are aged or doubtful, replace along with the condensor (save both...just in case. Also, it helps drive your wife nuts that you save all that useless junk and use up her Ziplock bags). Ditto on the plugs. Gap them correctly (not PERFECTLY - no one but God Almighty knows when they are PERFECT).
Now you have the electricity side of things squared away. The ONLY other thing that it can be (short of a worn-out something expensive in the engine) is air/fuel mixture. If you have been needing choke, it's because there is too much air in relation to fuel. The adjustments on the carb are simple. Download the KT17 owners manual from Kohler's website - the instructions are so easy even I could do it. If you can't find it, email me offline and I'll mail it to you. Next, check for leaks - start with the carb to intake manifold bolts/nuts. Snug them up. Not TOO tight - just tight. Don't reef on them with a wrench. If that mating appears good, move on. If not, remove the carb and replace the gasket between the carb and intake. Ditto the gaskets mating to the heads. Now check the play in the throttle linkage arm doodads (that's mechanic talk for any moving parts that pierce the carb housing and could allow air to sneak into the mixture pathway). They should appear stout and reasonably tight (not wobbling to and fro as if the mount holes were egg-shaped). If they appear good, now it is time to buy the CARB REBUILD KIT and install per the instructions that come with it. If not - and everything else is squared away - you probably have some worn-out doodads (more mechanic talk) and this is where my knowledge bank is tapped out. At this point, I would dismount the carb and mail it to a professional or just buy a new one.
Remember - these carbs are simple and reliable...like an M1 Garand. They are well-engineered and fussy only when you have them totally screwed up.
Other stuff that can be wrong...but unlikely...are sticking valves, etc. It's entertaining to worry about the worst case scenario but the problem is usually the guy with the flat-bladed screwdriver and the Kohler manual...
Ahh, that would be me...
