I am wondering if I need to have recent instrument and night time to be considered for UPS specifically, and all the majors in general. I flew plenty of instruments in my last military flying job, and a little in a 172 just before I retired, but none in the last 2 years. Other times:
4500+ TT (mostly fighter and T-38 time)
3000+ Turbine
2300+ PIC
1800+ IP
500+ in last year, 1100+ in last 24 months
ATP, B737TR, CFI, CFII, MEI, AGI, A&P
Oh, and I'm also working on a PhD as far as education goes.
But no IFR time in 24 months. And a couple of internal recommendations (only 1 that flew with me).

Should I get IFR recurrent in order to be considered competitive? How long might I have to wait for an interview? Am I even in the running?

go take an IPC and youll be current what else do you need with your resume youll be at delta in 6 months.

The 73 type will be a big red flag as they think you will bolt for SWA at the first opportunity. You should seriously consider going to your nearest FSDO and surrendering your 73 type if you truly want to work for any major other than SWA.

So If I had a 737 TR from flying the T-43, or from a previous airline job, I should surrender it??? I got that TR back in '96, when I was trying to get on with SWA. If UPS or any other major never hires anyone with a 737TR, they'd be throwing out an awful lot of applications. The 737 IS the most common airline airframe in the world….

Its flame bait AV9er. No need to worry about the 737 type.

What!!!! Dude, I know you are being sarcastic but SWA? Maybe 5 years ago but holy crap. Leave a major or UPS to go to SWA. Unless you live in base and you wife is the Chief Pilot then maybe a guy might leave

Totally incorrect.

You may get asked the question. Just have an intelligent answer prepared if asked...

Gee will a B727 T/R hurt my chances with a 737NG operator?

No, Custom Air Transport is long gone. Just like their hope of keeping the UPS/Menlo DAY flying.