It would be better to pursue othe Jetstream operators outside of Europe (Try Africa/South America/Asia). Also if like you said, it maybe a good idea to go FAA as there are still some Jetstream operators in North America. Paying for a 737 rating is just money down the drain unless you have a confirmed job in writing with an operator. There are just too many experinced pilots outhere at the moment with 1000s of hours on type.
I would suggest firstly, if you haven't done so already, get in touch with BAE Systems Regional Aircraft Division and ask them if it is possible for them to send you a list of all the operators of the J31/32 worldwide. If you then got a job with an outfit in some far away land, you wouldn't be bonded so you could then leave to go elsewhere when the job market picks up again in a couple of years.
Secondly, if you are that desperate to pay for a rating, then do it on an aircraft type where there would be less competition in the job market (e.g. EMB170/190/195). Or try and get a job with an airline's ops/crewing department or similar. Not only will you learn a lot there but it will keep you in contact with the industry and is a good way to get "a foot in the door" so to speak.
Thridly, I wouldn't worry too much about being "patchwork modular" now, most airlines would look at a candidate as how much of a training risk they would be. i.e. does this person have a realisitc chance of getting through the training? The fact that you have a MPA type rating already shows that you can do it.
I wish you all the best of luck.