Drill bits need to run much slower than routers can run. Suggest drill mills rather than drill bits. At higher speeds the drills will overheat and dull and lose temper.
I would then just mark, or use an 1/8th inch drill (jobber drill) the hole locations, then come back with a hand drill and finish them to size.
but then again, myself I’d try an 1/8th inch endmill, slow the router rpm down to minimum. and try a helical cut at around 60 ipm. That’s what scrap material for testing is for.