I'm not 100% sure on this but, you are asking about a Delta "connection" flight so if it was a Pinnacle operated flight, it would go Pinnacle pilots first, then, DAL or other DAL connection pilots (first who listed) then other 121 airlines (first who listed). I dont have my manuals in front of me but that's what i think.

You work for SW, if it was a SW operated flight i would think you would get it first even if you are the last to check in. Ofcouse i could be wrong.