Residual carrier tracking with PLL
I have been facing this problem of phase synchronization with my PCM/PM/SP-L signals as well, and found a temp solution by filtering away the residual carrier.

For carrier offset correction, there are two gnuradio blocks that work, the FLL Band Edge and PLL Carrier Tracking, but I found that the FLL Band Edge blocks works better together with the built-in Costas Loop block when dealing with PM signals with a residual carrier. This is completely from anecdotal experience though, and I have not done any proper characterization of the blocks performance.

One hacky solution of the phase synchronization problem might be to filter away the carrier of the signal before feeding it into the Costas Loop. This filter step should be after carrier offset correction, before Costas Loop. Since the presence of the residual carrier makes the IQ constellation of a Binary PM signal offset from the origin, filtering away the carrier will center the PM signal about the origin, and the Costas Loop PLL can lock its phase to that of a standard BPSK.

Rough Flow Graph:

PCM/PM RX -> FLL Band Edge -> Highpass Filter -> PFB Clock Sync -> Costas Loop -> BPSK Demodulator