Roz,
I did the same thing earlier this week. I had a rush order that included a deep scoop linen liner from one frame supplier and a stacked frame from another supplier on 2 large canvasses. I measured the canvasses, measured the foot of the liner to find out how much allowance to give for the stacked frames, and ordered everything UPS red label. Now you have to consider that the liner chops are coming from supplier A and both sets of frames are coming from supplier B and both suppliers are relying on MY accuracy with the measurements!
Everything came in Tuesday and the liners fit the canvasses perfectly! End of the good news!! The frames were 1/4" too short for a proper fit on the liners!! I called the supplier frantically and nobody had any ideas other than to red tag another set of long legs in for each frame and cut the short legs out of the long legs that I already had in the shop.
That would have killed my profit on this job so I decided to try something out of the box. Luckily the inner frame of the stacked frame combination was beefy enough and wide enough that I had an option to try. I set my table saw to the depth of the rabbet of the inner frame and shaved about 1/8" off each leg of the smaller frames from the bottom up. In other words, I added 1/8" to the horizontal size of the rabbet thus making the opening of the joined frame 1/4" larger. After dry checking to ensure that I allowed enough room for proper fitting, I joined the frames and they fit the liners like a glove!! And the outer frames were already chopped to fit the outside of the inner frames so they were a sure fit from the get go.
Bottom line, Roz, if you have a table saw and enough wood on your mouldings to widen the rabbet enough to accept the masonite, you could try the same technique. It may be better than cutting down the artist's mount board and possibly damaging something in the process.
(And ripping almost 4' long moulding in this manner does tend to separate the big dogs from the house pets!!)
(Picture that l'il guy with a stump for a thumb!)
Good luck, gal.
Framerguy