This is the exact problem I am having and in fact you explained it way better than I did in alluding to my grip woes in my earlier post. The grip acquisition is where I'm losing my time because trying to go too fast often results in, as you indicated, either a crappy grip and potentially not fully disengaged grip safety, or a solid grip but awkward leverage on the thumb safety. I also sometimes have issues seating my support hand too high and impeding the full motion of the thumb safety, but that has been easier to diagnose and fix.
Either way I look forward to any insights you come across as you're experimenting with your solution.