Leo,
the programming voltage on 2716 sucks, especialy older EPROM models like NEC,
that's why most programmers can't support them.
I can burn NEC D2716D on my top3100, i remember it was working on top2007 too
but only with External power supply (USB powered didn't work proper on older top models).
Typical 25V PGM works, it does work with 21V too for some never chips,
it is always a good idea to burn two, three times with same content.
Additionaly the top software does have (on second tab) settings for delay,
higher delay helps out too for some hard to program ics.
(some NECs 2716 works with 1ms, some need 50ms and 2-3 times overburning...)
As i have tons of older equipment here, i have of course some EPROMS too, starting from 2708 to 512.
So if you need working 2716 EPROMs (or even better 2732) let me know
BTW, top programmer are not that bad, sure software is not the best (well, the new topwin6 is already light years better)
The best model is of course top3100, each pins can be driven (the older or lower models can drive only some pins),
There is an open source software for top programmer too:
http://bu3sch.de/cms/index.html