350ES shifting problem when warmed up

Hey everyone - I've read a bunch of the ES shifting topics and I can't seem to find the answer for my issue.

It's a 2006 and it starts well and idles normal at first. I use it for about 10 minutes or so and then it starts idling very high, esp in neutral. At this point, it doesn't want to shift. I'm assuming because the high idle. In order to put the thing in gear, I pull the choke to bog it down and then I quickly shift. It's not ideal to say the least!

When I hit the shift button, I hear it trying to shift but nothing happens. Every once in a while the gear indicator will flash --- for an instant.

So the normal suggested fixes like cleaning the shift motor or replacing the level sensor don't seem to fit.

I was reading a post about the AIC valve maybe being faulty? Or maybe the air filter is clogged or I messed up when I cleaned it out and installed improperly somehow...

I just got this thing in the summer and it was used mostly for yard work where I would only use it for maybe 5 minutes at a time. I'm plowing snow now and noticing the problem.

The guy who sold it to me did mention that he tossed a new ebay carb in it because it wasn't running when he bought it off the last owner. He said the carb fixed it. I'll try playing with the idle more tonight to see if I can lower enough to be able to shift when warm but still stay running when cold.

Does anyone else have any other suggestions or more troubleshooting steps?

Thanks!