How do I clear the board of travel town of things that have reached their max level?

Are you talking about things that generate objects? Like beach bucket, picnic basket etc.

Those can't be sold but can be put into inventory. There is now one a separate one just for the producers. However, games a bit slow making more room for these after your done with them, (for now at least).

Ps. Occasionally, I'll pull put the ones that don't require energy to produce and sell items they generate to get coins.