Hugh, how about using acrylic sheets as a mounting substrate? Wouldn't that be less chemically invasive than Gatorfoam? Considering the size, I guess the significant weight difference might not be an issue, as the whole thing would have to be screwed to the wall anyway.
For the glazing at least, I would contact Cyro. If anyone could make a sheet that size, they could, probably with UV light filtering.
If not a continuous sheet, perhaps several sheets could be fused together with nearly-invisible seams. One way or another, I would guess it is possible to do prepare the glazing and mount boards and ship them directly to the installation site, where mounting & final assembly might be done in a weekend.
The frame could be custom finished to match the wall and attached directly to it in advance, including two rabbets with a built-in spacer between them -- one for the glazing and one for the mount board. Three sides may be secured in advance. After the mounted mural and acrylic are in place, the remaining rail (in pieces) may be added.
A huge, challenging job like this always seems easier to those of us who don't have to get it done.
Good luck. Will you let us know how it turns out? How about weekly updates?