A 121 training at the regional level isn't a walk in the park and could set these guys back a few years if they fail something. I had a military friend go straight to spirit and fail the checkride non AQP. They do old school MV style ride with only 4 full flight sims prior. Now that he has a fresh failure on his record he isn't getting any calls even though he is beyond qualified. I would shake the tree via having a perfect app, interview prep under your belt, and doing a career fair/meet and greet before bolting to a regional or similar type airline. The 737 type isn't going to do much to improve their standing.