I have explored some other starts, but the only one (except for the one above) that gave some nice continuation was this:
D R' D2 R2 //2x2x1 (4/4)
D L D //2x2x2 (3/7)
B U' B' //2x2x3 (3/10)
L F' L' //More blocks (3/13)
F' U2 F2 U' //Pseudo F2L-1 (4/17)
F U2 R U R2 F2 R F2 //All but 3 corners (8/25)
I've kept this as a backup partial solution, planning to quickly look for a 3 corner insertion in case I was left with only 5 minutes or so.
When I have finally found that "All but 3 corners and 3 edges" skeleton I had only 10 minutes to find insertions. I knew it was probably going to be better than the backup skeleton, but maybe 10 minutes weren't enough. In a competition I would have probably looked for a 3 corners insertion in the backup solution (I don't like risking a DNF, especially now that FMC is a Mo3 event) and be satisfied with a 30 moves solution (optimal insertion found by IF, but for a single corners 3-cycle it's pretty easy to find optimal insertions). But, since it was only practice, I decided to go for the (I thought) double insertion on the other skeleton. Both corner and edges were awfully placed during the whole skeleton, the best I could find was 7+8 for a 32 moves total, until right before the end, when I saw that the edges and corners could be solved with a pairs commutator after a setup move. In case you don't know, pairs commutators work exactly like corners commutators, but at some point you use a wide turn.
BTW, if you set the "other" option on IF, it finds an
even better insertion (while using only the "corners 3-cycle" and "edges 3-cycle" options it gives 30 HTM as the best solution).