Your story sounds very similar to mine. Two years ago I received a green card after a 12 year wait. Like you, I was stuck in the right seat with no upgrade in sight, over 7000 hours and no 4 year degree.
I decided against going to a regional and applied for a re-entry permit so I could beef up my resume a bit in my home country. I quit my job and was lucky enough to get a direct entry captain job on a regional jet. That wouldn't have been possible in the U.S. because of the 1000hr 121 requirement. I also enrolled in an accredited school in the U.S. and manged to finish a 4 year degree in 18 months (I had previous foreign credits I was able to transfer)
It's been about a year and a half since I received my green card and I just started job hunting again this week. I can now check the degree box and have 1000 hours in the left seat of a regional jet. I'll be attending a few job fairs this fall and winter.
Have a look at Thomas Edison State College, it's fully accredited and they accept credit from many sources. I was able to shop around for less expensive courses and transfer them in. I spent about $6000 total. It was nice to see the school listed on all the drop down menus at the airlines I've applied to.
On another topic, I got a couple of secured credit cards right away to start building my credit rating as soon as I got my SSN. If you haven't done that already you should.
Good Luck!