yea I've been thinking about how to go around that same issue you mentioned. Right now I have the back, sides, and braces glued. I can either:
A: glue brace H and the bottom, veneer the back, install the tube connectors, then finally glue the front on and veneer the rest of the sides.
or
B: glue the front, put 3/8" roundover all on all 4 vertical edges, veneer front/back/side, install tube connectors by reaching up thru the bottom, then install Brace H and bottom, veneer the top.
B will allow me to put a roundover on all vertical edges, whereas A will allow me to put roundover on front vertical edges only.