Now I know that there are many people who are geniuses and can solve the Pyramorphix.
You don't have to be a genius. How I did it, with simple algs I found myself:
Shape: Find two corners that are joined by an edge. First turn: pair the other two corners. Second turn: Put the two pairs opposite each other (to make the shape you have at 5:15 in your video). Third turn: Pyramid shape.
CP: 180 degree turns
CO: hold triangle pointing down and do (R' L)3 (R L')3 and (L R')3 (L' R)3 on each corner (hold the corner to be twisted on B. first alg is CCW, second is CW.
Centres: Two algs, one is simple and the other took me a while to find. First one: hold triangle pointing upwards, and do B2 R2 L2 R2 to switch F and D centres, and L and R centres. The next one is more difficult: again, hold the triangle pointing upwards, and do R B2, turn the four centres CW 90 degrees, then B2 R'. How I use these algs:
If you have a 4-cycle of centres, do the first alg from an orientation that will solve two of them.
If you have a 3-cycle, hold the solved centre on D and do the second alg.
If you have a 2-cycle, hold one on D and one on R and do the second alg.
If you have 2 2-cycles, do the first alg.
It isn't a fast method, but it's simple and it works.