TU,
I hate to disappoint you, but UPS and FED EX used to traditionally hire mainly ex-military pilots as you said but not anymore. They prefer narrow / wide body time, but they are hiring RJ guys like any other US major. Actually before the RJs took off as the regional choice, US majors hired at least half of the pilots with only Turbo prop experience. Yes the ex military always were the 1st choice but that pool had dried up long time ago.
There are a lot guys being hired these days by those 2 carriers that have no military time. Those days you're referring to are thing of the past.