The cowls on most of our cars are quite narrow, hence the 20" width. This also makes engine mounts easy. Once you are past the cowl, the width can increase, but why go to the effort? The rear suspension is often outboard of the rear frame rails.
By the time you add 10" per side for coil spring perches/ arms/ shocks you are at around 40". A 1938 truck bed isn't much wider than that. Negative offset on a set of reasonably wide rear wheels will close up any gaps between the tires and the bed sides.
I have built several single Z frames this way, and they have run down the road just fine. I don't suggest autocross in one, but for a simple cruiser, they work well.
If for some reason you need it wider at the rear, you could make the upper "deck" a subframe of sorts at the width you need.
Just be sure that the welds are up to the task. it's not just your life that depends on them!