Can't System Transfer Because Right Side of Switch Console is Dead.

My Switch is broken and is not allowing me to perform a system transfer to my Switch 2, which is frustrating because I really want to keep my save data.

The Switch can turn on and hold a charge but only the left joycon can be connected. The right side of the console is entirely dead, it won't connect to anything and I've tried docking multiple controllers and cleaning the docking area with no success. The left joycon is completely useless as it can navigate the home page but it can't select anything to initiate the system transfer. I've also tried connecting the Switch to a TV and plugging a wired controller into the dock, but the controller only vibrates and it doesn't register on the screen. I can't even connect a new controller because I can't select anything. I'm not sure if there's anything I can do. I don't want to waste any more time or money on this broken thing, but I have thousands of hours of save data I don't want to lose.

I'm planning to contact customer support tomorrow, hopefully they can do something but I honestly don't know what to expect. Should I just give up if it can't be resolved with customer support?