I made a 4x4 method for Petrus users. I can't see anything like it on the wiki other than Obli.
1) 3 adjacent edges
2) pair up the three necessary edges to make a 3x3x3
3) L3C
4) extend to a 3x3x4 by pairing up 2 necessary edges.
5) finish pairing up edges with a 3-2-3 type pairing method
6) EO+parity
7) solve with ZBLL, COLL+EPLL or something similar. Parity if necessary
Centres are easier since we have to preserve just the back, and edge pairing seems easy.
Look-ahead seems decent, and if you're good, you'll be able to look into petrus eo since it comes right after the edge pairing
I honestly think this is the best method I've ever proposed (not saying much)