(casual 1+ year bump incoming)
I've been thinking a bit about master pyraminx solving recently, and I wanted to share the method that I use for this puzzle. I find it very easy to execute, and if you're fast at pyraminx (unlike me), you can leverage that skill after reducing the puzzle to a pyraminx. See my video below:
The tl;dw version of my method: pair edges/wings, solve the reduced pyraminx, centers. I've been practicing the event for fun and have been able to get down to about 35 seconds with a few singles sub 25, and I've been using this for just about a week now.
I don't think this method is terribly novel, but I do think it's pretty powerful for how little you need to learn. The main thing that I have contributed is the 3-cycle algs - I couldn't find any good ones online, so I used ksolve to generate these. There were numerous 11 move optimal algs ksolve generated, and all were 2-gen! If anyone is interested in the full list of options, let me know, but I believed these to be the most ergonomic.
I've thought about how this method could be Yau'd: make a V, then pair the remaining edges, and start your pyra stage with a V already set up. However, I've run into a fairly major problem: the 3 move flip alg I use in my pyreduction method will break the V in any angle. I tried playing around to see if I could come up with a good flip alg that would not break a V, but I couldn't find one that was short enough. Given how many times you need to flip the edge, the possible benefits of starting with a V are seemingly outweighed by this, as well as the restriction of solving your first two wings in a V. If anyone has any ways to address these problems, I'd be happy to discuss them! The main efficiencies I've been trying instead now are to start making a couple 2/3-edges before inserting the third edge into the bottom layer so that the last 3 edges are quick.
The natural advanced extension to this would be to have some sort of alg set for doing the last 3 edges of the pyra solve along with the 4 centers. There would be a total of 143 cases for this, if I am thinking about that correctly (12*12-1). Definitely not going to spend time on that for a non-official puzzle, but it seems to be the natural advanced extension to this method.