I tried to stay out of this, but after post after post saying that carbs were easier to start (meaning fuel injection is difficult to start) I had to speak up. Starting a hot fuel injected Lycoming is a brain dead job. If you are having problems, then it is a pilot technique problem.
Here is all you have to do:
You shutdown your engine by moving the mixture to cutoff. Ignition off, master off.
Your start your hot engine by doing NOTHING!
1) Leave everything where it is.
2) Just crack the throttle (just like a carb)
3) Turn on the master and the ignition.
4) Engage the starter.
5) When the engine starts move the mixture to rich
I don't care what your instructor taught you. Do nothing but ignition on, and hit the starter. If you turn on the boost pump, and/or prime it, and it won't start, that's your incorrect pilot technique, not fuel injection.