One of my friend was on F1 and filed for TPS. His F1 got expired when he was on TPS. Then applied H1b, went Nepal for stamping and came back on H1B without any issues (he also took AP while traveling out of country just to be on safe side). He has also kept his TPS active by filing for extension.
So, the bottom line is you can change to H1B from TPS.

In my case, I was on F1 --> H1B --> H1B+TPS --> GC --> No issues
My spouse: H4 --> only TPS --> GC --> No Issues