You only need 750 Total time for a Restricted-ATP. Regionals will hire you with that, and you'll want to research who is most accommodating of RW experience
Regional FO is more of an internship than real employment for real professionals (ie who don't live in their mom's basement). It's dues paying for sure, but first year pay has about doubled to $35-50K recently, and some places are offering bonuses that may go higher than that. Military reserves can take some of the sting out.
Most majors do not hire R-ATP's and most or all are going to require at least 1,000 FW turbine, but that's low on the competitive spectrum. I'd guess you'd need about 2 years at a regional to get reasonably competitive.
Staying in to fly king airs might not get you a major airline job, you might still need to visit the regionals. Other folks probably have better SA on that than I. 3-4 years is a lot of airline seniority...I'd almost say if you're gonna do it, rip the bandaid off and get on with it now.
If you've had a typical or better mil career so far, you'll pretty much definitely get a major job sooner rather than later assuming you have no obvious personality defects.
Have you checked out APTAP.org?