Know exactly what your going through.
B777, the only real choice is SRTechnics.
I believe JHA are all restricted for B1.
A320 family, again SRTechincs.
QAC and AA are picking up the ball, finally. Aircraft access is the biggest hurdle in all this.
Hangar job will take some time, with some ATA's almost impossible to get the hours on.
Good lucks!!