My Aura One can be a bit finnicky with sync, a little more reliable with charging but I still wiggle the cable. And it's happening with cables I have labeled specifically as ones for the reader (some micro USB cables are charge only, so I label data ones that worked in the past).
I would imagine any shop that repairs smartphones and tablets could solder a new port. You might lose the water seal, but that's a small price to pay.
For syncing, I just run the Apache web server on my laptop, then just use the web browser under the Beta features. I set
http://192.168.1.3 as the homepage, my laptop's assigned WiFi IP, so it comes up automatically without having to type an address. It works for PDFs, ePubs, whatever. I haven't synced via USB in ages. I don't want to overuse the port.