No, the finish is not original. I received the guitar stripped and applied multiple (like, 12) coats of rattle can black lacquer, wet sanding between coats and then topped off with 3 coats clear lacquer. It's not fared well through the decades and whether I stay with black or another solid color, it's time to change it. There are multiple dings, scratches and chips as well as other blemishes that need to go.Apart from the area behind the bridge, is the black finish original?
If so, I would not refinish it. You could possibly smooth the rout seams and retouch that one spot, since it's already been altered. If you could get the original bridge pickup rewound it would probably be worth it. I think your instincts about getting a pickguard that looks close to original without paying all the money for an actual '65, is right. And I agree that you could probably get the nut grooves fixed.
Anyway, to my way if thinking, I'd restore in the least intrusive ways.