Accessing android device via ADB shell with broken touchscreen (can't authenticate)
I figured this out on my own. I solved this by installing Airdroid using an OTG USB adapter and a wired mouse. I then used the airmirror capability of the software to control a virtual mouse on the device. I do have root on the device, this may be significant to the operation of Airmirror. I could then accept the debug confirmation on the screen and complete the backups I wanted to do.