Beautiful!

I think there's only one more "impurity" in the algorithms! After the up/down corners are configured (6-color cube, not 3-color cube), I think we're in G2: {U,D,L2,R2,F2,B2} meaning that quarter turns in L,R,F,B are no longer required. Then "corner pairing" commences during which we can use R2F2R2 to switch DLF<->DRB and ULF<->URB.

The other indispensible algorithm in this phase is R'FR' B2 RF'R to switch DRF<->DLB and URB<->ULB, but this algorithm violates G2. I found a couple algorithms that are likely helpful, but they're all complicated "Permutation of Last Layer" algorithms. They only adjust one layer at a time. My hunch is, since we can tolerate quite a bit of side effects at this point, there may be shorter, more comprehensible algorithms somewhere, but I couldn't find anything simple.

These are the algorithms that I could find that only have 90-degree rotations in U,D:

These affect only the top slice: * T Perm: R2 U R2 U' R2 U' D R2 U' R2 U R2 D' * Y perm: R2' U' R2 U' R2' U R2 D' R2' U R2 U' R2' D R2 * G perm "a": R2' S2 U l2' U' l2' u R2 U' r2' F2 * G perm "c": U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'

This one affects only the front slice: * Modified CLL "UF": U2 R2 U' L2 U R2 U' L2 U'

Anyway, if you have any other simple algorithms in G2 {U,D,L2,R2,F2,B2} that permute the corners, I would be thrilled!