Is it better to get the 6950 and flash the BIOS?
What about a dual-monitor setup with my 1680 and the new 1920? Still sufficient with a single GPU?
You can run your basic desktop environment (browser, productivity apps, config tools, etc...) over multiple monitors with no problem using on-board, processor integrated or low-end graphics cards.
You won't be gaming across both of your monitors unless you have two or three at the same resolution. As a general (nearly universal) rule, games only run on multiple monitors with equal resolutions.
Gaming across two is not ideal and will put the crosshairs split between bezels. Multiple monitor gaming is best across three monitors with equal resolutions. This way the action in the center will be on the center monitor rather than split across monitors.