Well, First off, let me say congratulations for finding your problem and thank you for letting the group know what took place.
You are correct that the solenoid actuator is ONLY for HELPING with COLD STARTS. But, as you found out, it is clear that if not adjusted correctly, it can HURT with "runability". Which is going to be true for any choking or "cold start enrichment" system should it malfunction in a particular way. To put it in basic, good old boy terminology, the engine don't want no choke after it's warmed up.
I suspect that your choke was hanging up slightly in the "enrich" position and, after warm up, was keeping the desired air/fuel ratio from reaching the approximate 14:1 "metric" that we all try to achieve when burning gasoline.
The only thing wrong with the above stated theory is that, when you began this thread, you said that you had to "give it a little choke" to get it to run right at higher rpms. So, we all, or at least me, thought you were lean. So, I don't know. But, again, I'm glad you got it sorted out. And, even if you missed much of this season, you should be ready for the next and that's a comforting thought when sipping a hot cup-o-joe on a cold winter's morn.