I was in a similar spot with the exception that I got my ATP 'under the wire' and had some recent GA. Shop around for the regional you want, and pick them. It's like the stock market, hiring boom today but gas prices skyrocket and that could change, so puck something you can live with. Look at the fine print on the bonuses, some want payback of the first installment if you don't stay a year.
Your big competition right now is young guys from ND State end Embry Riddle who are smart and motivated but haven't flown anything bigger than a Seminole. Your experience and history of having completed a military training program is valued. So interview with one or two and pick your favorite.
It might also be worth a trip to your local FSDO if you're not too far away. It'd be worth the discussion, even though you're outside the 12 months, on how best to get the CL thrust removed based on past demonstrated experience. They're generally decent guys when not on the ramp asking for your papers and at RIC are largely former mil pilots.
I'm currently in sims at a regional, so PM me if you want the scoop on where I'm at.