I tried using the two tips you gave and was stymied for a long time, and put the puzzle away, etc. But today I sat down with a legal pad, an extra (single) pyraminx for testing things on, and I used those two tips (the 3-cycle and the two edge orientation) to solve my siaminx for the first time! So, I wanted to say Thanks! for helping me out with this one. This was the only puzzle in my collection that I'd never solved, even once. So it's kind of a Cross One Off The List moment.
I really have no idea how some of you guys are able to work out your own new algs, esp. such long ones. I mean, for comparison, I solved a Shengshou 9x9x9 yesterday, and the only time I consulted any notes at all was for the last two edge strips (and I used a 5x5x5 alg, adjusted for the 9x9x9x). That's it. The rest I did based on stored knowledge, not only of the 3x3x3 obviously, but of the 4-, 5-, 6-, etc. series. But if I had to come up with even 1 alg, totally on my own, with nothing else, I'd be lost. Was lost, till you helped me out. Anyway, THANKS MAN!!!