The key here will be the amp draw of the winch your looking at. Unless you have the upgrade alternator(40amp), your BX has a 14amp dynamo generator. You'll need to know the amp draw requirement at full load of the winch in question. Your battery has a reserve, but if your pull requires more than about a minute you'll exhaust your battery and possibly damage your charging system. I've got a Warn M12000 on my old woods truck and it draws about 80A no load and 435A at full rated pull(12000lbs). So, you can see the importance of knowing the electrical load at full draw in finding the right winch for your application. The other down fall to some of the smaller winches is the length of cable that they carry. I think most of them use between 25 and 50ft of cable. 50ft of cable would be workable, but 25ft doesn't leave you much to work with if your stuck very far from an anchor point. You can double the pulling capacity of a winch by using a block and tackle to compound your leverage but again cable length can be a concern here.
All said, I think a hydraulic winch would be a more viable alternative if you can find one to fit. Mile Marker use to make hydraulic winches but I think the smallest was in the 8-9000lb range. I know that they utilized the power steering pump to power them, but I don't know the GPM requirement that they used. Good Luck and let us know what you find out!!