"Is there any way to recover without a total refinish?"
Not to my knowledge. Paint? (I'm joking. I think.)
Curiously enough, I am currently reworking a 700 stock I built (my first!) from a nicely figured blank in the late 70's to replace the original press-checkered stock. Good project right now when it's 30 below outside.... and it had some "not quite right's to it... as well as nearly 40 years of acquired field-use "character"... It is due. Along with some others.
All kinds of routes you can go with here.
Cheapest (not necessarily easiest!) would be to chemically strip the stock (that press checkering is a PITA!), and refinish. After stripping (using a stiff toothbrush to "dig out" the finish in the dimples - you probably won't get it all anyway -be careful not to damage the "raised" portions), tape off the "checkering" and finish that separately with just a few coats lightly applied - which I would do on any checkering. Those dimples/grooves tend to fill up easily , cut or press checkering.
If plenty of wood, perhaps you can rasp/sand that abortionist press-checkering right out. I prefer plain stock to that crap anyway. After you chemically remove the old checkering steam the crap out of the press checkering to raise it as much as possible before starting to remove material if you go this route. May (probably) not come out well anyway...
I have guns with press checkering, plain wood, and real checkering....they all shoot (and pretty much carry) the same- it's a fricken HANDLE after all. You may just want to go with a "character" stock (yeah, I've got one or more of them too!!!!), that is protected from weather and the hell with looks. You can be the "ugliest gun in camp" guy.... Go totally counter to all those other doofuses. with their closet queens.
Or replace the stock with your choice of "aftermarket". You can probably pick up a factory take-off (with real checkering!) pretty cheap on amazon or from campfire ads. It might be a straight drop-in giving good accuracy, but I'd do a glass bed on it anyway. (All my guns are so bedded, factory or not). If it needs refinishing, a cut checker stock is way easier than press-checker, anyway.
Go with a synthetic, from Ramline (cheap!) to McMillian. Again, epoxy/glass-bed it. No matter what they say about "drop-in", glass bedding will improve it's accuracy.
Sounds like you probably don't want to build one from blank-scratch or a "90% inletted" piece.
The latter really means 90% of the extra wood is gone, but 90% of the fitting work is yet to be done.
Good luck - and you shouldn't be keeping a firearm in any kind of lined case unless it is quite breathable. I don't anyway. Also don't store it cocked- striker springs can weaken over time.