Sorry for the necroposting, but I noticed that the original question was not answered.
Yesterday and today I tried to program a few blank TMS2516JDL devices using my TL866CS, thoroughly erasing them with UV eraser between attempts. I can attest this programmer cannot reliably program these devices, as they use 25V programming voltage.
I used the following parameters:
TL866CS SW version 6.85
Vpp = 21.0V
Vcc verify = 5.0V
Vdd Write = 5.0V
Pulse delay = 1000µs
I hope this helps someone in the future.