As you've already realised, with SAS and bmi both being * Alliance, you are very unlikely to get a status match.

You might get something from BA, but it is more likely to be silver than gold. If it's really bmi you want, consider choosing an intermediary programme (ie get a comp to KLM and then use the KLM membership to get a comp to bmi). You'll need to check the relative comping policies of the different airlines (run a search in each forum for "comp" or "status match"). Generally, bmi seem to be fairly generous in this respect. BA not so much.

In terms of how you go about it, you need to phone up the airline you want to move to and explain your situation (ie "I'm Gold with SAS but I've had some really bad service from them recently and I'm considering moving all my business. Obviously, I'm worried about the temporary drop in status and I wondered whether you could match my status with you?"). If they're receptive, they'll usually want some kind of proof when you send in your application form (normally nothing more than a statement from your current FFP showing what status you hold). Never heard of anything as dramatic as chopping up your card and mailing it in...

Hope that helps