Let me add my .02 about the plane sitting just to the right of "Willit Run" in the WWII Gallery, their Bf 109G-6. At the time the Silver Hill team restored it, the true identity of that aircraft was indeed a mystery- they knew it was a captured G-6 brought over for testing, but didn't know which one as all the normal dataplates had been souvenired off of it. So, they picked a representative scheme from a photo, selecting an aircraft whose configuration matched that of the 109 in the collection (G-6, short antenna mast, D/F loop fitted, FuG 25 fitted)... they selected "white 2" of 7./JG 27.
Well, it turns out someone DID eventually track down the identity of that aircraft, and it's actually a rather famous bird... it's WNr 160756, formerly "yellow 4" of 3./JG 4, piloted by French defector Uffz. Rene Darbois who flew the aircraft to a British field in Italy on 25 July 1944. I had the good fortune to get full run of the aircraft back in early 2006 courtesy my friend the late Tom Dietz, who was the curator of the German aircraft collection at the time, and I was rather dismayed to see that the paint was peeling off in sheets from the uppersurface of the starboard stabilizer, and other wear was clearly evident elsewhere. I spoke with him about repainting it in Darbois' markings (no small undertaking, as I./JG 4 used a lot of locally mixed and Italian paints to camouflage their aircraft to match the arid Italian landscape), and his response was that he'd be all for it but they were having enough issues with funding trying to keep the lights on, let alone repainting aircraft which were already on site.
I don't know who succeeded Tom after his untimely passing, so I don't know how familiar they are with the history of this bird or if they'd be willing to revisit the scheme, but there was at least one guy in a position of responsibility in the NASM who was willing to put that aircraft back in it's original markings. And frankly, I think that's probably true of most of NASM management at this point, given how hard they worked to put their Fw 190 back into it's service markings, as well as the Gekko, Seiran and so forth, but I can't say that with absolute certainty.
All I know is, if they DO repaint the Mustang and they don't want to put it into the markings it originally wore, I want to see it in a 359th scheme.

Lynn