Taxi, maybe, if the queue isn't too long. There is generally a few minutes wait for Uber, at least.

Since you are HBO (handbag only), connecting the inter-terminal AirTrain is relatively easy, and the interval between each train is quick.

Honestly, assuming your BA flight arrives on time, and you are not stuck behind a long line at immigration/customs (you shouldn't - T7 is not particularly busy at that time of the day), you would be fine with going with DL. Of course, you know your walking pace and navigating through airport terminals better than anyone.

Edit: forgot to mention, as a US citizen, you don't have to fill out the blue form anymore. You can queue and complete your entry info at the machine (though not the GE kiosks). There will be someone in the arrival area to direct you to the right place. Look for the US citizens area.

Good luck!