Well... I have spent some time playing with this & it seems that the trick is the frequency at which the monitor is driven. So long as you can drive it at 67, 72, or 75 Hertz, it works, & seems to work fine. Of course, the frequency is tied to resolution, so I can't get anywhere close to 1080p where it needs to be since all the higher resolutions are locked to 60 hz or lower.
Immediately prior to installing the 5770 card, I had a 5550 in there that worked fine with a DVI connection, but the 5550 had actual DVI connections rather than the mini displayport connectors that this unit has. I have already swapped the cables & the adapters with no change.
I have thought about trying to edit the driver file or the EDID data to allow me to try to run this monitor at 67hz, but that is a band-aid since it works at 60hz with the other card. I suppose I could get a VGA adapter & use it that way, but I would really rather understand the problem & fix it rather than to keep buying parts.
These viewsonics are about to be retired in favor of some HP ZR24W's (that support displayport natively) but it would be nice to not be handicapped until they get here sometime next month.
If anyone has any suggestions that will help, I would love to hear it.