Modernage and Lamont can do that size in fiber. They will, however, want to make a drum scan. If you choose to go fb it makes no sense to mount to masonite as it's not archival. Dibond is the superior choice. $2k is a good estimate.
Recently a lab opened up in boston that specializes in large fb. Might be worth the research as then you won't be paying nyc prices.
Face mounting makes no sense as you'll get orange peel effect on anything other than an "f" rc surface. They're trying to up-sell you.