Cutting 3" oak on my little bandsaw is a challenge, and then sanding the
marks out without ruining the shape is even harder.

A coupla ideas re. sanding:
1. If you take the inside offcut from your rail, cover it with a thin
piece of neoprene or maybe felt or something, and use that as a sanding
block, it should follow the inside curve of the rail just right. (i.e.
use convex offcut to sand concave rail face)
2. Have you tried a sanding drum in the DP? It'd be a pain to take
multiple passes with a short drum, but Lee Valley has a "large sanding
drum" that's 3" tall. Their support bearing is very nice also, which
reduces lateral load on your DP keeps the drum square to the table. I
own both of these and recommend them. (Stay away from HF sandpaper,
though.) Setting up a fence or dowel or something at a fixed distance
from the drum would give you a guide to keep the rail thickness
consistent.
Good luck,
Andy