Go to Microsoft site & download the offline tool, make sure you get the version that covers all versions for factory reset. Copy that file to flashdrive. Insert in USB port of console with the XBOX off. Next step could take a few tries, press & hold sync button, while still holding sync button press & hold eject button, while still pressing sync & eject press & hold power until it beeps a few times. That tells you that it detects USB stick & the file on it. If it doesn't beep 3 times (I think its 3) you didn't do the button presses quick enough. Doesn't always fix but worth a shot. FYI the restore takes a while so don't be worried if you don't see anything on the screen for a bit. Don't power off while it is restoring, be patient.
I believe the latest update makes it so you can remap the controller buttons. I have a similar problem (no left hand) so I can appreciate the need to move a trigger function. Update (01/11/2016): Doing a little research online, check out oneswitch.org.UK, there are multiple links for USA based sites that do custom controllers for people with disabilities and war veterans. There is also a link to email for questions. Hope it helps.
http://support.xbox.com/en-US/xbox-one/system/offline-system-update-diagnostic-tool. Follow this link & go down to USB factory restore option. Had the same issue & this fixed it. A little tricky getting the Xbox to recognize the USB stick. I had luck pressing sync button first & hold button, then eject& hold,then press & hold power button & listens for the beeps.