If you're in the pool, there are ways to maintain currency and competency without taking a flying job someplace. You essentially have a golden ticket that thousands of us are trying to get. Pursuing any kind of additional aviation job is a lot of long-term risk for very little short-term rewards.
If you feel confident passing training at either of these places (Atlas or PSA) you'll pass training at UPS. If you feel like you need to build your skills, then you definitely don't want to do that at a carrier which could derail your position at UPS.
So why take the risk? There are lots of avenues to pay your bills that won't hazard your UPS job.