Recruiters will always try to get pilots current on type because it is seen as saving a buck on induction training. Although this can be a fallacy, and in fact being too current with some other company's different SOP can actually be counter-productive, if that is what they want you are probably wasting your time dealing through normal channels.
So, there are two possibilities.
1. Find a way to bypass the recruiters and get in direct contact with the chief pilot - often the chief pilot is not kept fully informed of applicants who may actually be his preference.
2. Think about going somewhere in the short term where they may be less selective (i.e. a bit desperate). Some less salubrious third world country perhaps. If you can handle the poor conditions for a year or so, you could get the recency on type that you need to move somewhere better.