LoL, I just figured this out and was going to post the solution as you did. Although I didn't have to change the BLEND_MODE to fix the funcup. Maybe I should add that anyway?
Thanks to everyone that chimed in. Quikslvr, as you, this has bugged me for a long time with certain cars.
Now the other cool thing that this fixed was (and I made a post inquiring about this a few weeks back) but it also fixed the smeary TAA issue in addition to the dissapearing under-car shadow.
I'm stoked, man. There are a ton of cars I need to fix now.
EDIT:
@Quikslvr, have you found a SHADER replacement that has a little bit of tint to it? I've replaced the small windscreen on an old vintage f1 car, but the ksWindscreen is so clear that it is hard to tell there is actual glass in the little windscreen. No biggie, but if you know of a way to replace with a tinted or darker glass, lemme know. It's the one in the pic below. The little windscreen has no edge or bezel which makes it harder to tell there is actual glass in the mount with the shader replacement implemented.
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