Well, I've found that it can be done. I used my trim iron and kept it moving constantly along the edge of the covering. The smaller 'shoe' on the trim iron keeps the heat from building up too much. I think I will brush a little paint on the joint just to make sure it stays down.
Actually, now that I think about it, it probably would have been better to iron on the Monokote and then paint the plastic. That way I wouldn't need to worry about melting the paint and having it stick and burn on my iron.
Oh, well, live and learn...