What I find so funny (not laughing at you VentZer0 btw) is that I prefer manual starts too as a bit of a challenge and when I started this mission, I only started 1 engine! Is there two in the UH1?
My sequence is a little different (not saying it's correct), but if you want to try:
1. Battery on;
2. Starter on (wait for 12% torque);
3. Throttle to idle (wait for 65% torque);
4. Starter off (wait 15 seconds);
5. Throttle to Full.
Off I flew without a problem.