Professor Pyraminx

I am pretty sure this one is well documented, but I wanted to see what I could do without looking. What did I try and how did it work out for me?
1. Centers. The 3 pieces around the fixed center.
2. Corners. The 3 edge pieces that go with each corner.
3. Edges that are in the center of each edge of the puzzle.
4. The... uh... edge pieces with 2 pieces, one on each of two sides, that are connected on the edge of the puzzle. I wonder what I used to call these.

On the left you see the scramble I started with. Steps 1 through 3 worked easily enough. Sort of. At first I lost some of the center pieces on step 2, but once I figured it out, it was easy. In fact, steps 1 through 3 can be done with Up Replace Down type moves and The Move. I don't think step 4 can be done without messing up the edges of step 3. I was right about that. See?

In fact edges from both steps 2 and 3 were scrambled. Solving those was easy with The Move. It is solved. So let's compare what I said before with how I solved this time.
2020 solve:
1. Centers using Up Replace Down or The Move
2. Weird edges using 8-move Commutator
3. Edges using The Move

I certainly was thorough with it when I solved it years ago. I named edge piece type and even faces and slices. I came up with algorithms to do pure 3-cycles and 5-cycles of center tips. I came up with 3 different solution strategies. The weird edges can be solved simply at the expense of center tips. The center tips can be solved just like 4x4x4 centers! So either doing that or doing what I did yesterday requires solving 12 pieces using an 8-move commutator and slices.