Update: one of the lamp holders is flakey, so forget everything I've said, who knows when it was working and not working.
Warren, the ballasts are 58 watts so "should" have enough power to run three 15 watts assuming they'll light up. S2 starters...I think the ones I have are S1s? I'll have a look at them when I get home. If I have to run 6 ballasts in the end, that's fine, I can scrounge up what I need, I think. But, if I can manage to get three 15s running on a 58 then I can get away with just 2 ballasts.
If it works, I'll use it, if it doesn't, I'll try something else.