I did it like this:
2. Solve centres.
3. Solve 4-stickered edges (corners?). (This is similar to solving the Pyraminx)
4. Solve 2-stickered edges. (There is a simple sequence you can use in combination with setup moves. Let's call two adjacent 4-stickered edges (corners? But actually for this stage centres... woah) U and R. If you do the sequence R2 U2 R2 U2 you will see that you are doing a 3-cycle of 3 of the 2-stickered edges without jumbling them.)
Hope this helps direct you. I'm thinking of making a guide video on YouTube at some point. This is a really cool puzzle and my first one that jumbles!
Funny: I solve it with step 2 and 3 reversed.
When You use a quarterturn set-up move (on a (not)3x3 face) for the (U2R2)2 alg, you affectively have a 3-Cycle you can not perform on a Gem I without jumbling. I think the puzzle can always be solved without jumbling.
any suggestions for a straight forward terminology/notatiion?