The Falcon color is a bit of a goofy one. Doing white over a black pre-shade might do it if the coats are kept light. But that is a tall order with rattlecan finishes, considering their high flow design. I agree that straight camo gray is too brown in shade and a little dark. Light Gray is another possibility as it is lighter in shade, but the problem I encountered using it over a black pre-shade is it shifted the color too blue. So I needed to mix it with camo gray to counteract the blue properties a bit.
Is the Insignia white you mention on Tamiya's AS color line paint rack? That may work. It really isn't a white shade at all and I think Tamiya was trying to represent a grunged up white on a Navy jet after it had been at sea for a month or so (Navy jets from the 1960s and 70s started out gloss gull gray over gloss white, but end up very flat after a few weeks). Insignia white SHOULD be just a straight white color. Tamiya cans have some REALLY nice spray tips on them and I think you could shoot it light enough to get a good coloring over a black preshade.
To me, the Insignia Gray looks a bit on the light side, although it seems to look about right for a Falcon color based on the original 5 foot ANH model as oppsed to the ESB one. Plus, washes can always be used to darken it down as in my experience it is easier to darken a base coat then to lighten it (drybrushing can only go so far). It might also be worth checking out some of the MIG filters as they could be used over the top to get the hue right. Someone else also mentioned Tamiya smoke tint and that could work as well. But I would go VERY light with it if using it as a wash and give the model a layer of gloss first so it doesn't spiderweb into the finish too bad. Even a normal wash of a gray based paint over Insignia white may give you the look you want.
BTW, here are some examples of the colorings I used to give you an idea of how the weathering altered the shades in the end. All pictures were shot with the same camera and the same light sources (flourescent countertop lighting up close with more normal room lighting above and behind the camera):
Original Falcon color attempt, FS Light gray over black preshade
Second attempt with 50/50 camo gray and light gray mix
Closeup of the color patches before weathering began
A very diluted Tamiya smoke tint wash added over a gloss coat (turned out more semi-gloss)
Here's the final look after flat coating and pastel chalk work