I have heard a heavy hint from a simulator trainer that if you were to fail the power supply to No.1 N1 gauge, you can fool the system into thinking No.1 has failed so the LGTU will then be powered and raise the gear.
I think the option to actually shut down and then relight is reasonable if you are up an alley with no other way out. It's not traumatic for the engine and has such a reliability of relighting that it's OK to do. If the only other alternative is to bust limits into a mountainous nasty place, I'd do it like a shot.