You should definitely be fine then with the 1250. Personally I'd probably push it to the 1040 even on a separate PNR, but that's my preference and risk I'd take!

The re-check desks are just the other side of customs after international arrivals and the domestic security is about a 5 minute walk away. In the past I have had Comair agents phone up with 25 minutes to go if it is OK for me to run to the gate (which I've done once).