I'm pretty sure that it uses a generic driver like Windows does and limits you to only 1024x768 unless you force it to another resolution on boot. I don't think this is the case, I think the GPU is failing to initialize because the voltages, timings on memory, and signalling between the 5770 and 6870 are very, very, very different.
There are very few reasons to flash a BIOS/VBIOS on a PC. I know you're probably feeling pretty crappy about this, but a point has to come out of this, even more so since I administrate a fleet of Apple laptops at work.
There is absolutely no reason at all whatsoever to flash anything on a Mac that isn't in the form of an Apple update, EVER! Even if you do manage to get the BIOS switched back, it's very possible you could have fried the GPU since both GPUs run at different voltages and such and just attempting to use the different settings could damage the device.
I wish you the best of luck, keep us updated on your progress. Worse comes to worse, now that you know that video card is removable, if it is bricked you could attempt to replace it, but worry about that when you get there. Cheers.