Scag Turf Tiger/Kohler Command Pro 27 Frustrations

2009 Scag Turf Tiger
27hp Kohler Command Pro (I don’t know the model number as the sticker has long since disappeared)
650 hours (653 hours now, bought used 22June2018)

Starts strong, runs great for about 30-40 minutes then begins to lose power while blades are engaged. I can release the blades and let the sucker stand for a few seconds and the engine begins to sound “right” again. Then…once I start mowing again…same thing, engine loses steam. I can let is sit for 30-40 minutes and go through the whole routine of mowing for 30-40 minutes with no problem before the issues start again. There also seems to be an oil leak near the dipstick.

Here’s what I have done:
Compression check: 120psi on both cylinders. I’ve heard this number doesn’t mean much for these engines because they have a built-in release valve.
Replaced spark plugs.
Drained all the previous owners gas and replaced with “clean” gas.
Checked for spark with inline tester both resting, under load, and when it is acting up. Clean spark. At least that what the tester tells me.

Could it be:
Ignition coil? I know there will be a consensus that the DSAI thing is junk and my problem. My ignition coil number is 24-584-36. The kit that is supposed to “fix” this direct ignition problem does not show compatibility with my model coil number.
Worn/sticking valves? If so, can this be rebuilt with long term success or will the problem eventually resurface?
Carburetor?
Tiny rip in the seat?
Yes, I know I have posted this on other forums.

Thanks, all!