Others closer to the problem can weigh in but I suspect you need to be current to get called at the moment, as a fairly low time civilian (unless you have extensive prior 91/135 turbine experience). Hiring has slowed, very much so for regional FO's and stopped for some ULCC.

For the majors do you have a degree?

Also does "about 1,000 121 SIC" mean at least or slightly more than 1,000? If so you could almost certainly get hired very quickly as a regional DEC. Money would be good and 121 PIC would be good. If you have slightly less than 1,000 121, you might be able to get hired as-is and get the 1,000 121 while on captain OE... you're actually the SIC while doing CA OE with a check airman. You'd have to ask the regionals, but they need captains bad.

And yes face time with recruiters is a good thing, at the very least they can tell you where you stand.