I think the diagonal cove cut is probably the easiest way to get the concave surface on the sides.
I might even make a jig to mount 6(?) sides between centers and belt sand the outer convex sides. The jig would have a flat base at each end with shallow straight mortises to receive the square outer ends of the side pieces. I might even use pieces long enough for two or three (or four?) sides per piece then cut them to length last. Might do the cove cut before cutting to length.
Lotta red dust being created!
The glass grooves should probably be cut prior to shaping the sides.
Tis early for me so consider that my mind may not be coherent(yet).
So fodder for the noggin anyway.
