Yeah, messing with those sections you highlighted was next. Whatever is going on there, it isn't evenly spaced. I'm tempted to idealize it a little. I'll see what I can come up with.
The way I have it now is created from trying to directly trace the visible sections and then sliding them back into place afterwards. Inherent perspective distortion could definitely account for stuff not lining up perfectly even after taking out most of the distortion in Photoshop first.
One thing that was super helpful was the circular UFP seal. When I was taking out the perspective in photoshop, I simply simply kept stretching and shifting it until the seal became perfectly circular again. Otherwise I'd have no idea exactly what the correct width and height proportions would be. At least not as easily.
12x8 size seems to match up best as far as the proportions matching even measurements, which seems to be the modus oporandi of the prop crew on TNG. Having the Statue confirm that initial guess solidified it for me. I'll do a physical mockup soon to double check everything. Nothing beat a real life test to make sure something works.
One odd thing is the "Upon notification..." line at the top doesn't feel like matches the blurry, barely visible scrawl from the screen cap. I've slid that text around and tried it at different sizes and it just doesn't feel like it matches. Since it's barely visible I wont sweat it too much.
Another interesting little bit is the TNG Starfleet logo on the left. There seems to be a little bit of a gradation to the white of the oval as it approaches the Delta. I guess there is a slight halftone dot of some sort applied to it.