Edit: okay, so I started "Final Piece" and got the "... Greater Power" trophy after using the Blast Core.
FYI... I may have found another potential glitch for purchasing powers without losing your points. I will try to confirm on my next playthrough. Basically, I was grinding out UGCs to build up my XP. I was still active in a UGC mission when I received the in-screen prompt that I had enough XP to purchase my "last" power. I immediately went and purchased it. When I finished the UGC mission, I still had my XP available.