With only 40+ years experience of working with stainless I hardly dare add any advise
Stainless comes in many specs, some are just a bit more 'difficult' to drill than mild steel, some are a lot more difficult and for the home hobbyist could be a real bitch. As above, you need to centre dot the hole, FFS don't use a flat bottomed cutter in a drill press, cobalt drills are good to use but HSS will probably suffice, your mains drill will probably be too fast, if you have a battery drill this might well be better, as it's a one off use whatever lube is to hand, duck oil, engine oil, or grease.
Slow speed and plenty of cutting fluid, use a small pilot first. One thing do not let it get hot or it will harden then be near impossible to drill.
Don't bother drilling anything contact v-mach send your trigger unit away and ask for a precision trigger job the unit will come back with a new trigger blade and it will be set up so presice you will think you are firing a new gun this mod is amazing and is well worth the money -- after its done your trigger will never require adjusting again the screw will be removed and a blank is put in its place
Use a cobalt drill bit or get a pro to do it.
the right angled screwdriver seems the easy answer to me!
Plinkerer and Tinkerer