As an ex Recy Mech to a serving one regarding work on the rigs.
There is heaps of info (on this site) regarding work on the rigs, and I know of a couple of lads that are working on one now. However they had to go through a whole raft of (pretty expensive) courses regarding H&S and whatnot, before they could even sniff at employment.
I reckon if you fired off a highly impressive CV (and it never hurts to try) I reckon you would get a BFO pill, if they even bothered to reply.
Sorry, can't help you with anything else, I'd had enough of anything to do with recovery when I came out and changed direction completely and haven't free-spooled since.
Use the search thingy top right, type in 'oil rig' and wade through it. Good luck mate.