I am a 6300 hour part time contract pilot. I'm finding that full time jobs are elusive for me (not sure why, that's a whole other story). I have been contemplating a 737 type to possibly give me an edge in the airline world. Is it worth exploring or is the fact I have no 121 time a bigger problem? I do have extensive experience in the 135 world.

I think type ratings are almost worthless without "time-in-type". They want actual line flying experience normally. Anyone can get a type in anything, but that doesn't really make you qualified to fly it. It can enhance a resume. Southwest requires it. I'd say its not worth the price unless you will get something from it.
Good luck.

I can't imagine a single contract job that would hire you with no time. None.

Also, to compound your issues, you admit that you have no airline experience. If you have $5000-$15,000 to burn go for it.

What is the cost of a 737 type these days?