It's a beautiful coin as is, I would not crack and I definitely would not perform any type of conservation on it (doesn't need it). You have to remember an important thing with the TPG's. They mainly grade using eye appeal and luster (in that order, #1 & #2). The lack of contact marks and a good strike rarely influence a grade enough to boost it.
The "woody" part is a major deduction for all TPG's. They think it detracts from the eye appeal. Not only do I like the woody look, but that means I typically get a better coin, IMO.
Have you considered sending it in for a re-grade? If it doesn't upgrade it stays in the same slab. Nothing ventured, nothing gained. Of course you are out real money for the grading fee.
If it went from MS63 BN to MS65 RB, then I should be able to get 5 times what I paid for it. But then I'd have to sell it. And then I wouldn't have it any more. So, I probably won't. Getting a few folks here to say it may be a higher grade will have to do. But I think I may take it to a nearby dealer who wholesales higher-end coins and get his in-hand opinion.