I know you said that you were advised not to do the BMAT, but I found that there was actually less competition with it as people aren't able to apply tactically with it (as you both sit and find out your score after application) so you have a far better chance of getting in as long as you do averagely well.
(Also, I know this is a bit last minute, but it might be something to consider for your 4th choice if you don't mind some extra work)