Thanks ijgordon

In fact, by Saturday 1-Dec it was back to a shuttle bus on the congested roadway to go from T4 to T1.

I can add that, while contacting the accessibility email listed above resulted in no help at all (not when I asked nor when my spouse’s excellent assistant tried) except for a circular reference back to the webpage, the actual human being providing the wheelchair service was fantastic, calm, professional, and just truly great at his job, (I think his name was Allan.)

From my single data point, even if you have two separate tickets, wheelchair services will get you all the way from your Delta arrival gate at JFK terminal 4, to T4 baggage claim for your checked suitcase, and on the shuttle bus to T1 and your check in counter for your next (international) departure’s airline. (From there we had to wait to check in our big bag when the counter opened, so 2nd airline called new wheelchair attendant for the TSA gauntlet and onward to the lounge.) So that part was all good.

Wheelchair attendants #2 and #3, post-lounge to gate, were adequate and good respectively, but the wait times at T1 were too long and added a moderate amount of stress.

(The overall terminal experience at T1 did remind me why I’ve avoided JFK for decades, and I won’t be back any time soon if I can help it,)