Here's my $.02. I have been with 5 121 carriers (mostly not by choice), and hiring seems to boil down to two common denominators: quality flight time and career progression.
Even if HR recognized that you were furloughed from your last carrier, they will not like the fact that you have gone back to flight instructing -- it will look like you've gone backwards rather than forwards.
In my estimation, you have two choices: you can wait for the "more qualified" (read: higher multi time) pilots to make it through the system and get called; or you can improve your qualifications by accruing some multi time (preferably turbine).
I get that ITE it has been virtually impossible to get a multi job, let a lone a 121 gig. If you choose to accrue more multi, you'll have to be extremely flexible, think outside the box and dig through the weeds to find that job that will get you over the hump.
Finally, I think the 121 resignation can be explained given the flight time and experience you had at the time -- plus, a lot of time has expired since. Work on an interview answer that is concise, unemotional and up front about the situation and don't make the issue bigger than it is. IMHO the resignation is not the stopper, your lack of quality multi time is. Good Luck!