Scotts S1642 hesitates then dies when PTO engaged

I have a Scotts S1642 with Kohler Command 16 (CV16) spec 43526, with the Walbro carb. A condition started 2 months ago that I'm not sure how to diagnose or repair. The mower would start fine, but when I engaged the PTO at full throttle, the engine would hesitate. I could lower the throttle, and the engine would resume, and then I could slowly go back to full throttle and cut the grass. This progressed into when I used the lawn mower after about 30 minutes, the engine would hesitate then die. I have to repeat the whole process again, and finish the lawn. I rebuilt the carb, which didn't seem to help. I took the carb off again to make sure I didn't miss anything, re-cleaned, and reinstalled. Right now, the mower starts fine, runs strong, and will go thru full throttle range as expected, but when I engage the PTO, the only way I can keep the engine running is at lowest throttle setting. If I throttle up any, the engine hesitate and dies, and if I disengage the PTO, the engine goes back to running perfect.

I went from having to engage the PTO at half-throttle, to engine cut-off after 30 minutes of use, to now engine will only stay running with PTO engaged at lowest throttle setting. Anything higher throttle and engine shuts off. Disengage PTO, engine runs fine.

What could cause this condition?