Update:

Plywood panel has a small amount of twist that could cause issues with my intended use, so I decided to make another, but with a new idea on getting a better (tighter) joint.

The simple shapes are easy to clean the long grain edges of the char, but the ends are more difficult. I use a small block with some 120 PSA grit. With the end grain, there is a chance of splintering off the sharp corners with the sanding block.

So what I decided to try is only cutting through the veneer along the long-grain sides and just leaving a shallow line along the ends.

This gives me a place to register a sharp chisel to cut the veneer at the line.

Still not perfect, but better!
These pieces are 3/8" wide.