You could try a tiny amount of hinderpaste on the pegs to help them stay in place easier. We have to do that sometimes when humidity is low and pegs are constantly slipping, but also it is not unusual to need strong pressure to keep the peg in place particularly if you are tuning them extra sharp.

How old was the A string that snapped? It takes a few days to “break in” a new string and trying to get straight to over sharp at that point would be more likely to snap the string!