How to motivate myself to do more than the bare minimum that is required of me?
Wow.

While I was reading your question, I was thinking "did I just wrote that myself and erased it from my memory"? I just started my PhD in Mathematics, having obtained my Master's Degree last semester..

You pointed several problems we face as students of Mathematics who are trying to become researchers. One of them, which has drawn most of my attention, is this 'repugnance' from the details of something you already been through. I usually deal with this situation as follows: some of those details (in a proof, in a exercise, etc) are either too boring or too hard. If they're too boring, I usually make sure myself that I can remember them should I need them (in a exam, for example). If they're too hard, I usually try to convince myself that it won't be in the exam of the subject I'm studying for (this does not mean that I study only for exams!).

Whenever I am done with some subject, I choose another one to keep studying. As a PhD student I usually feel that there are a lot os subjects I should have mastered and a lot other which I should have some knowledge of. I usually use those 'confliting states' to switch to another subject which I have chosen by myself (not related to the lectures I'm attending). For example, I'm now having Several Variables Holomorphic Functions and Riemannian Geometry courses, but also reading a textbook of Theory of Foliations since I'm sure I'll need it next semester. It's not my priority though.

Now, keep in mind that you're not striving for the minimum at all times. Reaching a PhD course after obtaining your Master's degree is a really big deal. Are you really sure that A's and B's are the minimum that keeps your advisor satisfied? My advisor complimented me on my grades from Master's Degree Courses once, and it was full of B's, two A's and one ugly C!