I had an interesting talk with...
...my local FAA FSDO Airworthiness Inspector yesterday (received my Repairman's Certificate), and the subject of Operating Limits came up. He stated that after the original Phase 1 test period, and after the "certifying" statement is placed in the Logbook, the paper work that (three pages of Operating Limitations in my case) no longer apply and no longer are needed.
I was somewhat confused and we continued the discussion, but the end result is that the Op Limits paperwork state Phase 1 in the title, so that is where it applies.
I realize that different FSDO offices can interpret the regulations differently, but he did make a point. I also showed him where certain items of the OpsLim "could" apply (paragraph 21) forever. He stated that he would check with Oklahoma City and get back to me.
As for the original question, any one can place their aircraft back into Phase 1 Test. You do need to contact the FAA FSDO office and let them know that you changed the prop, have a new w/b, and update the FAA paperwork to indicate the new prop manufacturer and s/n.
As an example of what "changes" constitute a return to Phase 1, my FSDO inspector actually used a new prop as an example. He said most likely a return to Phase 1 would be for a 5 hour duration, followed by a new entry in the aircraft logs stating that the aircraft was found to be controllable through all speed ranges, etc., etc., etc...