Mind you, this bug is preventing me from running a graphical interface on a computer. I would say it is critical/severe.

More info is required to help us help you

What Machine? X86_64? i686, i386
What Videocard (I can guess from the xorg log that it is an ATI R600, but what if xorg is identifying the card all wrong?)
Does this card work with other live libre distros?
Does this card work with the current lxde_dual live Parabola iso?

64-bit Intel i-generation.
AMD Radeon HD 5770.
I don't know.
I don't know.

As some AMD cards are problematic (Require non free firmware to function fully) with libre software. Please try with a couple of libre live DE ISOs (Parabola, Trisquel ) and see if they can reach a graphical environment.

This will help us pin down Hardware issue / configuration issue / actual bug in Parabola

Well obviously a Parabola xorg-server bootup would result in the same thing. What if I boot Trisquel tomorrow?

I just booted Trisquel 8.0 MATE Edition and X seems to boot fine.

Good to know.
Can you please send a copy of the xorg log from Trisquel for Comparison.
Thanks.

I get this error on a different machine too, same graphics card.