Unfortunately I had already purchased, and cut, a nice piece of 3/4" plywood for the face and top. Will the difference in weight between these two make a significant difference?
Couple of things. First, the weight difference for that one part won't bee too great, but it's way too easy to add this little bit of weight and that little bit of weight and some other little bit of weight and wind up with quite a lot of dead, useless weight to haul around. I'd ditch the 3/4" ply and drop down to 3/8" ply for the top, quarter inch ply or hardboard for the front.
As for framing, I might well keep the 2x2 stock for my attachment points to the fiberglass shell walls, but would use a tight-grained, finish grade (something like Hemlock, but wood types available vary region to region) 1x2s placed on roughly 16" centers for most of my framing. If you glue these 1x2s to the underside of the 3/8 plywood they'll be more than strong enough to support your weight; tight-grained woods are both stronger and lighter than the more common 2x2 stud grade stuff. Also, remember that, as long as the wood doesn't have any rot or knot holes to compromise it's integrity, wood is really very strong. So strong that cheap, stud-grade 2x10 lumber on 24" centers supported 12' apart can comfortably handle the weight of a refrigerator
, king-sized water bed, or grand piano.