Rednex
If our illustrious Moderators read this and reply I think they'll probably advise not. My two penny worth is:
1. I understand most companies want a type rating plus 3-500 hours on type.
2. Not doing the type rating with a specific comapny means you won't have learned their Standard Operating Procedures, which may be a draw back. ie they'll put you through a conversion anyway.
It's a difficult one but I think you may be better off keeping the CPL/IR current on a MEP and keeping/obtaining other work to live off until the break comes.
If it's any consolation I have nearly 5000 hours (2300 Mulit Jet) and I'm unemployed too. I will keep the IR current and not risk a 737 TR.
Best of luck and network as best you can.