The papi does not have the same calibration requirement as the ILS glideslope. The airport is "free" to place it after let's say 100 ft down from the actual TDZ. Where as the ILS has to be calibrated using the touchdown zone.
Secondly the minimum eye height over threshold might not be applicable to your type of aircraft.
So I would say yes you can continue without papi, not following the ILS anymore below sounds like something learned in flying school, how do we fly CAT II/III if the gs is not reliable below 300ft?