Hi,
The problem is not the programmer but the EPROM chip itself. May be too old.
Erasing the EPROM set all bit to 1 (ie, all bytes should be FF) and programming set only bits to 0.
Here, you try to program a 3A (00111010) value, but the verify (read) after programming return the value 7A (01111010).
This mean that the 6th bit failed to turn 1 to 0. Most of the times, it's because the component is too old.
All UV EPROM have a limited number of cycles(erase/program) and may be, this one has exceed.
You can try to program again the chip. Indeed, the missed "1" can be still turned to "0".
Try to program again, but disable the "blank checking" option before.
This will program the chip, but without testing the virginity (not testing the bytes for FF value).
The TL866 is unable to program the basic 2716 with Vpp 25 volts, but there is no issue with the 27C16. So, should be working with this component, unless if it has exceeded its life time / cycles.
But looking at the config, I see Vpp - 21 volts.
This is normal for a classic 27C16, but take care that your 27C16 are not B model. For 27C16B chips, the Vpp is 12,75 volts.
If the Vpp voltage is correct, then, you can try to increase the Pulse delay.