Many higher-end devices (such as PIC24) implement it in hardware for the reasons you mention.
Yep. Unfortunately PBP just doesn't support the PIC24, PIC32, or dual-core pentiums..;o) And, for this particular application, that would be like hunting rabbits with a Sherman TANK. Honestly.

You just-do-not-need-to get-that-complex for such simple wireless communications, and it really does NOT require any PIC type beyond what PBP supports.