FYI to anyone who finds themselves in this predicament:

The hospital will not refer you to a 3rd party service they have zero affiliation with. That would be a major liability/ put them at risk of being sued.

I've asked my PCP, the specialist, my insurance, the hospital and the doctor performing my procedure if they could refer me to a service. They all confirmed they do not know of any such service.

They can recommend transportation, but not a chaperone who will sign your liability release forms.

Essentially, it's not their responsibility to find someone willingly legally liable for you. They just do the procedure.