Not sure if this ought to go here or in the big cubes discussion thread, but it's a slight variant on redux, so I'm going with (possibly) new substep. I've tried 2 solves on 6x6 and 1 on 7x7, and both are pretty much in line with my regular redux times. I suspect with practice it could get better than redux, although it's almost certainly not useful for 4x4 and 5x5, and might be no improvement at all even for 6 and 7.
Steps:
1. Solve 2 opposite centers
2. solve remaining 4 centers in any order, on 6x6 disregard color scheme
3. Pair first 8 edges with freeslice, using R2, L2, F2, etc. (assuming edge pairing on E rather than M) to flip edges rather than using an alg to maintain center orientation. Place solved edges on U and D faces, as normal.
4. Solve centers, using slice or wide moves and the same R2, L2, F2 moves as for edge pairing. All center pieces will be in 4x1 (for 6x6) or 5x1 (for 7x7) bars.
5. Solve L4E as usual
6. 3x3
Pros:
Lower movecount in F8E pairing
Possibly easier to find pieces, since you normally wouldn't see pieces on the D layer without a cube rotation.
Cons:
Adds a step to regular redux
Potentially more difficult to track unsolved edges, especially after the first 4 edges are solved, and would normally be hidden on the bottom.