I don't own an Ice-9, but I think I have come up with a commutator-based solution.
Using this reference for notation, R and L turns are always 180 degrees, while F turns in increments of 90 like a regular 3x3 as F, F', and F2.
ice-9-reference.PNG [ 180.08 KiB | Viewed 778 times ]
1. Note that the center of the 3-fold axis on the "top" and "bottom" are stationary and define these as solved.
2. Intuitively solve the corners and the pieces adjacent to those stationary centers as if the puzzle were a triangular floppy, fixing corner orientations trivially with corner turns.
3. Solve the 12 triangle pieces adjacent to the corner pieces via [3,1] 3-cycle: [R L R F R L R F']
3. Solve the 12 edge pieces pure via [7,1] 3-cycle: [R F L F L F' R F R F L F' L F' R F']
There may be a more efficient solution, but these were my first ideas. Please confirm if my algs work or not because I cannot say for sure myself.