1) Jenny 100: "The most likely explanation for the difficulty seems to be that the people who made the games tested them with the VESA that was current at that time..."
I agree that this is the most likely explanation. And the problem is, as you know, even more complicated - there are not only new VESA standards, but new hardware and new Windows systems. For example some VESA games have problem on NT/2000/XP that can be solved by Ken Silverman´s NOLFB VESA patch http://www.advsys.net/ken/build.htm
. For other VESA games is this patch useless. Every problem is rather unique and no universal solution for all problematic VESA games (let alone all older games) exists. It is sad that people who made those games and have access to the source code are often no longer interested in big problems that gamers have with their products (of course, company may be no longer existent, but people usually live) and probably never read forums like this. There are a positive exceptions like LBA WIN patch http://lbawin.c0m.st/
and people from Revolution at least gave the source code for Beneath a Steel Sky to the fans so now we can play that game again on the current systems.
2) Jenny 100: "When you played it with a Geforce 2, were you able to get higher than 60 Hz?"
Yes, there is a solution. Shareware program Unirefresh (link is above) or freeware VBEHZ http://www.informatik.fh-muenchen.de/~ifw98223/vbehz.htm . Both work even in Win XP NTVDM (Virtual DOS Machine) but with VBE 3.0 cards only (like GeForce2). If your card doesn´t support VBE 3.0 there still may be a way, SciTech Display Doctor. But SciTech must support your card. AtiRage 128 is supported in SciTech 7.0 beta. However, I´m not sure if all VESA games will work with these utilities.
3) For gamers who don´t know how to tell the refresh rates in DOS games: Many modern monitors have OSD (On Screen Display) menu where usually is info about the current refresh rates. Access to that menu is often through OSD button on monitor.