With the recent discussion on the LCBM method, I thought I'd take another look at this and came up with a couple more ideas for it. First of all, I added an algorithm for swapping 2 adjacent corners on each layer to the correct sides. Still need to work out algorithms for the remaining cases(diagonally opposite corners on each side, opposite on one side and adjacent on the other, 3 corners on each side, and all 4 corners on each side).
Secondly, instead of starting with the belt, what about first placing all the bottom color edges in the D layer, oriented but not necessarily permuted correctly(permutation will get messed up in later steps anyway). Then continue with the belt. Placing the D layer edges like this should probably only take about 4 or 5 moves(don't know the exact number but obviously <= the number needed for a true cross and being color neutral should reduce this a bit as well) and this eliminates the first couple parity cases described in my original method and simplifies many of the other remaining steps as well.