I'm a bit of a 4x4 n00b so take this with a pinch of salt.
Anyway, I've been playing with this, and it seems like a Roux-style start is quite a sensible way to solve the 4x4, possibly better than using pure reduction. Using Roux for the the finish obviously isn't suitable for speedsolving bigcubes because of the reliance on double M-slice moves. Instead the n00b Roux-Fridrich hybrid can be used for the finish. The steps would be:
(note: M-slice moves here really means stuff like rR' or lL')
Step 1: Solve LH + RH Centres
Step 2: Solve LH 1x3x4, and RH 1x3x3, and any pair in FR slot (normally a lucky pair)
Step 3: Finish Centres, using M/U
Step 4: Pair final 6 dedges, using M/U and FR slot where necessary.
Step 5: Finish F3L (solve the FR slot and place DF/DB)
Step 6: OLL/PLL
... milking the VC
Using this approach seems to have some pretty nice ergonomics and lookahead advantages because:
* There are no rotations.
* All dedges are paired in the M-slice, using M/U moves.
* Last four centres are solved in the M-slice, using M/U moves.
* The maximum possible number of dedges are solved at the beginning (before centres), when full freedom is available to pair them - good for efficiency and lookahead.
* Leaving the FR slot free gives an easily visible location for finding pairs, and allows enough freedom for easy edge pairing. The only hidden dedge locations are in the M-slice - good for lookahead.
Does anyone else use this kind of approach to solve 4x4, and/or what do you think about it?