During an IPC, is there any alternative to doing a precision approach?
As far as I can see, there's no way to avoid flying a precision approach during an IPC. 61.57(d) says:


  The instrument proficiency check must consist of the areas of
  operation and instrument tasks required in the instrument rating
  practical test standards.


The instrument ACS requires a precision approach, as you said, and it's also in the checklist in AC 61-98C, Currency Requirements and Guidance for the Flight Review and Instrument Proficiency Check, and the FAA's accompanying instructor guidance. So I think it's fairly clear that the FAA requires it as part of an IPC.

As for limitations, the FAA's AC 61-65 Certification: Pilots and Flight and Ground Instructors doesn't mention any that are specific to an instrument rating. I've never heard of a 'non-precision only' instrument rating.

I can only suggest that your friend finds another aircraft. The 'good' news is that once he's current again, he can maintain currency indefinitely with only non-precision approaches and avoid another IPC.