By making certain snapshots useful for all three trophies, I was able to use one less snapshot to get all trophies in 32 snapshots. I'm 90% sure I can't get it down any further but if somebody else manages it, I'll be pleasantly surprised!
It's seems barely possible... the issue is bringing back both a ladder and blue key without wasting frames requires the merge come from frames 9-16, which is after the golden key door.
I'd either have to waste a frame to make a branch (otherwise I can't merge backwards in time), OR I need to get two red keys and a green key without using frames on timetravel in order to physically go backwards to the golden key door. (which is blocked by a red and green door, that I skipped using a ladder so both are locked, and the only nearby greenkey is locked by a red key).
...it might be possible?