Speaking about getting a higher rpm on a free turbine engine prior to introducing fuel, I was told once that if you left the propeller tied in place during the start(we used to tie them down on the Twin Otter to keep them from rotating in a strong wind while shut down), you could get an extra 1 or 2% rpm. Never tried it of course, has anybody else.
I know this sounds ridiculous as a procedure, but keep in mind that this is for remote arctic and antarctic ops where what has become a weak battery may only allow one attempt and then you are stuck on the cold tundra or ocean ice along way from anywhere. Then you release or cut the rope after start.