The damaged pads on the top side of the board won't be an issue. They have no connection to any other trace on the top of the board, and you can see the connecting traces on the bottom go from a ground connection to both pins. So as long as either pin has a good solder joint, there will be more than enough connectivity for a good circuit.
Besides providing a ground for the plug's case, the other main function of those vias is to provide a strong mechanical connection between the jack and the circuit board. You've got more than enough solder pad on the bottom to give that, so you're fine in both electrical and mechanical aspects.
Onward and upward! C'mon back and let us know how it all turns out. If you've been taking pictures, why not continue and once you're done you could use them to create your own iFixit guide to your USB-C mod. It's easy, fun, and you'll certainly have the appreciation of anybody else who wants to do that mod.
Create a new Guide - iFixit
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