Recently I've been poking the shared holes with an awl before stringing to make sure they are fully opened up (both sides of the grommets) and my life has been a lot easier since then. I'm not sure if this is a good practice but it works well for me. What do you guys think about doing this?
You are doing the most correct way. Only when we forgot to or lazy to enlarge the shared holes before we start to string, we have to find some way to conquer the shared holes problem. Or just leave the shared hole problem to be an unexpected challenge for fun.
I never can make any progress with a string mover, I don't know if I'm just not pulling the string in the right direction. The best (and worst) for me is using an awl to create a gap in the shared hole (I've broken strings a few times from this), but when I reach those really stubborn holes, nothing else seems to work!
I've just ordered a Yonex badminton awl, which may be better than the cheap (and nasty) Pro's Pro one.
I never can make any progress with a string mover, I don't know if I'm just not pulling the string in the right direction.
String movers work great, but every hole has an optimal direction in which to pull to make clearance for another string. The optimal direction is sometimes downward and sideways and sometimes upward and sideways. Inspect the hole closely to see what direction is best. It is often counter intuitive on what direction is best. Also, once you decide on the direction of pull, make your pull as close to the shared hole as possible so as to achieve maximum deflection of the blocking string.