Hmmm... Eugene has an Adaptive Equipment Rental, including at least one full handcycle, as well as the Dragonfly mentioned above. Photos look a bit different, so perhaps an older model of the Dragonfly.
https://www.eugene-or.gov/SlideShow....ment%20Rentals
Portland administers their Adaptive Cycling through the Bike Share program.
HOME
It looks like they also have a few handcycles,
OUR BIKES
Apparently they have a couple of Excelerator handcycles. Perhaps here?
| Top End Wheelchairs | Performance Wheelchairs
These appear to be complete chairs, and not just add-ons.