I think that could work but I'm not sure if it's as good as existing methods for Petrus. I think that instead of doing a 3rd cross edge you could do the final edge in the beginning 2x2 and then move that over after so there is more freedom during a modified 323. I also think that doing something like this but with Hoya could also have some promise.
Can you elaborate? (Maybe a numbered list would help)
Here's something I came up with:
1. Hoya F4C (L/R centers, B/D centers).
2. Blockbuild a 1x3x4 on the D layer, and make sure it touches L/B/R, pairing dedged when needed.
3a. Pair 3 dedges simultaneously (like in 3-2-3), making sure to only pair one back slot.
3b. Do an F move, then pair up another 3 dedges. You should now have 3 dedges unpaired and 2x2x3 done.
3c. Somehow simultaneously do L3E and EO. Maybe an alg? I would imagine it wouldn't be too many.
OLL Parity: Use a shortened alg that doesn't preserve Last Block.
4. 3x3 stage with only 2-3 shortish steps! (LB, OLL, PLL or LB, ZBLL).
3x3 stage is massively faster than Yau 3x3 stage because F2L is only 2 pairs (plus an edge, but that takes no time at all), has super easy OLL, and then some normal PLL. The dedge pairing might still need some work; I'm no 4x4 expert.
EDIT: I forgot how to English.