So I have three more comments here based on that.
First, finding somewhere to get positive reinforcement is going to be difficult because that’s not based on the school or the department. That’s based solely on the personality of the individual professor you choose as your advisor. That’s difficult to know a priori.
Second, if you are trying to work diligently to master something, that’s definitely something you can do in graduate school. However, throughout graduate school you are working your tail off only to learn, just as you had that “Aha!” moment, that there is so much more you don’t know beyond that. There is always more to learn and get better, and that can be very frustrating at times. You never feel finished yet at some point you have to know where to draw the line and publish. If that is something you think would perpetuate your feeling, then that could be a deal breaker.
Finally, no professor is willingly going to let you hang around for 4 years getting a master’s degree. That’s a waste of their funding and it implies you will be working very slowly, which makes you even more difficult to fund and more difficult for them to write new proposals. In the end, if you want to stay that long, you are much better off putting in the extra year or two and working at a more acceptable rate toward a PhD.