Old UV EPROMs are very unlikely to feel their age (unless they have been erased many times or been abused, ESD damage etc), they live in nice cozy hermetic cerdip packages so are not subject to moisture for instance - although you should check that the pins are clean. Back in the day, programmers had as many programming algorithms and VPPs as there were EPROM manufacturers, often more. I wouldn't be surprised if modern cheap programmers had lost a lot of the subtleties of programming these old devices.
I'd stick with your vintage Advantest (for these devices).