As it turns out, most (though not all) of my troubles were the result of errors in Eagle libraries for component footprints. In particular, the DB25 connector I used, was a mirrored image version. The fix for this, was to mount it on the bottom of the board. Once that was fixed, I could get it to read EPROMs, but I still could not burn them.
That troubleshooting took several days. It involved hooking up the scope and checking signals. In the end, it turned out that a transistor (BC141-16) had the collector and emitter swapped in Eagle. Once that was corrected the programmer worked beautifully.
Lesson Learned - don't trust the libraries in Eagle to be 100% correct. Verify them before you send out your board to be made up.
Now it is on to burning EPROMs for the Mod 80.