Having thought about this more, I would redouble, and I think pass is the second choice, 3S third, and 3C not in the running. I would pass at IMPs, since redouble could be a disaster. At matchpoints, not only is the occasional negative telephone number not as important, but a spade lead rates to hold in the overtricks even when it doesn’t set something, and that matters a lot at matchpoints.
I think it’s clear redouble simply asks for a spade lead and does not promise general strength (though you should have somewhat reasonable hopes of making 2S or holding it to one off against a game). Analysis of why is in the last two paragraphs.
I do not particularly want to be at the 3 level in spades. 2SXX scores better except when both are disasters. We have already preempted them, and we have surprise distribution for defensive purposes. Let them play guessy-guess. The other problem with 3S is that it could be a raise on all small cards. If LHO bids 3N over it, I’m not so sure I’m getting a spade lead.
3C only implies spade support if you are playing McCabe (2NT forces 3C so you can sign off with a misfit) in this situation. That would be a reasonable agreement, but you probably don’t have it for purposes of this problem. I think 3C is just running from 2SX (not forcing like it probably would have been if RHO had passed). Note that even if 3C shows spade support, it in that case asks for a club lead, so I wouldn’t choose it, since I think it’s more likely I want a spade lead than a club lead.
A general-strength-showing redouble has to be reasonably sure of a plus in the redoubled contract and has to want to suggest penalizing them if they bid on. It’s very unlikely to hold such a hand on this auction, with both opponents already having shown decent hands. (Negative double of 2S, unlikely doubling a simple overcall, promises a decent hand. Fewer than 10 points will be quite rare.) In the grossly unlikely event you are staring at 15-16 HCP without spade support on this auction, then your best bet is to pass and listen. Either RHO has 7-8 cards in an unbid suit, or they are simply overbidding (in which case, let them keep overbidding, don’t warn them).
On the other hand, redoubling to show a lead is a hand you will hold often, since it’s safer than raising. You only need to have reasonable hope of making 2S–it does NOT need to be a favorite–since 2SXX down 1 may be a good sac (and also beats 3SX down 2), and since you figure to gain from the intervention in the likely event they bid on. On this hand, redouble is the only call likely to get an ace underlead against a diamond contract. Even though you can’t ruff the 3rd round, partner may be cashing it if he is on lead after trick two.
