Redneck usually gives good advice and I'd trust him about the slight refinishing and tung oil suggestions .....

But twas me if I had the time, I'd try to to locate a "new" (and factory-stock) butt plate to replace the miscolored or damaged one. If you're trying to keep that antique .410 original, doubt the cost for a genuine replacement butt plate would be that much.

My first shotgun was a .410 M370. I HATE single-shot .410's!

But Model 37's in good shape are indeed heirlooms or collectors' pieces. GOOD LUCK!