After solving the bandaged pieces, I placed the edges. It is an easy task and seeing which ones that need to flip is so much easier for me when they are in place. Using 90° turns of the white bar and the red bar, pairs of edges can be flipped. More specifically, with orange up and yellow on front, M2 (F U F2 Ui F) (Ri F2 R F2) M2 flips UR and FR. It also 5 cycles corners. The first (section) does the flipping, and the second (section) puts them back in place. During the solve I don't really put the edges at UR and FR and do the algorithm. It doesn't really matter which side the one on top is on, and it doesn't matter which side the one on bottom is on. Turn the one on bottom that needs flipped down with either F or Fi. Turn the one on top that needs flipped to UF. Swap them with F2 and they are flipped when the bandaged pieces are put back home. After the edges are flipped and solved the hard part comes—the corners.
During the experimentation and analysis stage I came up with 4 key sequences that can be used to solve the corners. I'm thinking that perhaps with further work the method could be refined and simplified, but I'm ready to move on. Annie wants to help me tile a new puzzle. :D
S1: M R U2 Ri U2 Mi = FR > UR > UL; 18327; x3 pure cycles 12873; doesn't move 4
S2: M Li U2 L U2 Mi = FL > UL > UR; 18274; x3 pure cycles 17842; doesn't move 3
S3: M2 Ri F2 R F2 M2 = UR > FR > FL; 14723; x3 pure cycles 12437; doesn't move 8
S4: M2 L F2 Li F2 M2 = UL > FL > FR; 14238; x3 pure cycles 13482; doesn't move 7
In practice you don't have to do all the M moves between sequences of these cycles. Just move the white bar either to the top or front, wherever it is needed.
Stringing these together in different combinations yields pure corner 3-cycles. After doing the first two, choose the third one by seeing what needs to happen to restore the edges.
S1, S2, S4 cycles corners 1 > 3 > 7
S1, S3, S2 cycles corners 1 > 2 > 7
S1, S4, S3 cycles corners 1 > 4 > 3S2, S1, S3 cycles corners 2 > 4 > 8
S2, S3, S4 cycles corners 2 > 3 > 4
S2, S4, S1 cycles corners 1 > 8 > 2
S3, S1, S4 cycles corners 1 > 2 > 3
S3, S2, S1 cycles corners 1 > 8 > 7
S3, S4, S2 cycles corners 1 > 7 > 3
S4, S1, S2 cycles corners 2 > 7 > 8
S4, S2, S3 cycles corners 1 > 4 > 2
S4, S3, S1 cycles corners 2 > 8 > 4
When looking for the edge flipper I made a happy little discovery.
M2 F U F2 Ui F S3 S2 S3 S4 S1 S3 S2 Mi. Of course there are M moves between the sequences when necessary. What does this do? It flips UR and UF, and it twists corner 3 clockwise and corner 7 anti-clockwise. That means if you do the whole thing twice the flipped edges get unflipped and the corners get twisted again, so the net result is to twist 3 anti and 7 clock. Granted, it is a lot of work to twist a couple corners, and if the corners aren't at 3 and 7 it requires some crazy setup moves, but it worked. Perhaps someday I will look at Pendulum again and find a better way.