(1) Does BGS regrade the graded cards in its own holders?
Yes
(2) What are the odds of bumping the grade to a pristine 10?
Near 0
No one can tell if that card “should” be a 10 from the photo you posted, and grading is just not super consistent at that level of subgrades. You can crack and resubmit over and over until you get a 10 if you really want to try, but I wouldn’t recommend it unless you honestly believe that it’s currently a misgrade. If it were as simple as “it’s only 0.5 subgrade away”, then the countless cards out there in a similar situation would all be 10s.
The Giant Professional Grading Thread may be a better venue if you want feedback on specific card condition.