I've seen return trunks/runs created by panning sections of floor joists instead of using ducting, sort of what you are talking about doing.
I think that isn't an approved way to do it everywhere or as wide spread as it used to be. In addition if you are going between floors, you have fire code concerns to deal with. Usually openings between floors must be sealed and/or blocked to prevent the speed of fire spreading. I would check with your building inspector before doing that.
From a technical point of view, yes it should work because you are essentially creating a duct using a wall cavity.
In my house we had a similar issue, with ducts and ceiling height.How bout just putting a 2x on the left to screw sheetrock into and glue the rest onto the duct. We're talking 1/2" here and u can do 3/8" if u needed to. Just my .02