The trick to re-orienting pieces on basically any puzzle is to first find a 3-cycle for those pieces. Then find a way to re-orient one of the pieces ignoring everything else. If you can get your 3-cycle and your re-orientation routine to overlap by only one piece then you can re-orient pieces pure.
For the Helicopter Dodecahedron, first some notation:
helicopter_dodeca_notation.png [ 17.96 KiB | Viewed 1387 times ]
Now a [1,3] 3-cycle [A] [B C B] [A] [B C B]
helicopter_dodeca_3-cycle.png [ 10.53 KiB | Viewed 1387 times ]
Now observe that [m n o p q]
will re-orient the white-green-cyan piece in place:
helicopter_dodeca_dirty_re-orient.png [ 10.49 KiB | Viewed 1387 times ]
Finally combine. Do 3-cycle, dirty re-orient, undo 3-cycle, undo dirty re-orient:
helicopter_dodeca_pure_3-cycle.png [ 10.44 KiB | Viewed 1387 times ]
This construction is the same for all twisty puzzles. If you understand it than you can re-orient any pair of pieces on any twisty puzzle provided that you can find a 3-cycle and a appropriate dirty way to re-orient a piece.
As for your center triangles problem -- I spent some time trying to create this situation and was unable to. I'm pretty sure it requires jumbling moves. Even if you can use non-jumbling moves to fix that, if you don't see an easy way to do that then you should probably use jumbling moves instead.