X windows has the ability to take a mode line. It used to be that you had to pretty much define them yourself, now they have an internal list that they try by default, but in my case it was failing pretty miserably, but only for one mode. So I got out my calculator and came up with a mode line that worked. Just put it in the Monitor section on one line and change all the references from 800x600 to 800x600x60 in the Screen section.
ModeLine "800x600x60" 41.02 800 840 968 1056 600 610 615 644 +hsync +vsync
The original was the following, which didn't work for me.
"800x600" 40.00 800 840 968 1056 600 601 605 628 +hsync +vsync
Basically I increased the vertical blanking period and increased the dot clock to keep the frame rate at close to 60Hz. The math to figure out the horizontal sync is 41.02*1000/1056 = 38.845 kHz and the vertical is 41.02*1000/1056*1000/644 = 60.32 in Hz. The on screen display of the monitor lists 63.9kHz and 60Hz.
Interestingly enough another computer with the same LCD had the same original mode line but with a 39.97 Hz dot clock and it didn' thave any problems. The graphics card in that system is a SiS 315 PRO.