There was a bargain price PCI TNT2 on eBay showing the same symptoms as OP.
I was close to buying that TNT2 after researching these issues, and the TNT2 was ultimately bought by @giantenemycat.
My opinion is that the root cause is more likely in the analog stage Barium Titanate capacitors than in any RAMDAC.
Principally, a RAMDAC generates each pixel sequentially left-to-right. That means full-line darkening (pixels to the left) would require a RAMDAC to do time travel and I'm not buying that - so it's not the RAMDAC.
What I'm seeing in all the photos is whole lines darkening (or brightening) to match an average. Looking really closely at the artefact, I think each line is showing the average brightness of the preceding line. To me that looks like some kind of moving average bias in the analogue stage after the RAMDAC.
I have done some reading and I think the fault can be better described as "baseline shift/droop in the analogue stage of resistance and capacitance".
Healthy PCBs stay within 0.0v for deep black to 0.7v for bright white, but afflicted cards are drifting. Sometimes the voltage drifts too low (e.g. -0.3v to +0.4v - darkened) or drifts too high (e.g. +0.3v to 1.0v - brightened).
According to one manufacturer of ceramic capacitors, Barium Titanate capacitors are known to show DC bias and ageing characteristics - and that is a very elegant explanation for everything we know about this issue. The challenge now is in identifying analog stage Barium Titanate capacitors, testing, and replacing them.
My hypothesis suggests all affected cards should produce a near flawless output of 3D rotating camera scenes where the brightness of the preceding line is continually changing thus pulling the voltage up and down and blending together.
Milestones [ MOS 7501 → 68030 → x86(P5/MMX) → x86(K6-2) → x86(K7*) → PPC(G3*) → x86-64(K8) → x86-64(Xeon) → x86-64(i5) → x86-64(i7) ] * original lost