I suffered the same problem as you with the warm GTSIO. So much so that I was nearly knocking the battery out.
A Kingair pilot walked over who apparently had a 1000hrs on 421's and showed me this technique which works for me :-
Throttle 1" open
Mixture ICO
Fuel pump Low
Engage starter and bring up the mixture simultaneously.
DO NOT PRIME.
Hope this works for you.