I know UPS does pickup, but if they are unwilling to pack them properly to their specs, you are SOL.
You could ask them if they have an employee who for a fair fee would pack them on off-hours and ship them, probably UPS, FedEx (more expensive).
Greyhound busses take packages, I had something large (an antique dresser hard to pack) I bought on ebay shipped to me that way, and something I want to sell the way it is packed, the PO or UPS won't take it, a mirror, not as much glass as windows but glass). I'm not ripping it open and packing it again. Greyhound only wants them wrapped, they don't seem to care how, and do have insurance you can pay extra for, prices competitive, the only option for some things now.
Maybe somehow you can work something out that way. Stay on them. I know they don't like to mess with customers who don't spend a lot of money, not cost effective for them but would be a good will gesture to try to be more accommodating.
Good luck!
Thank you so much for all the insights! I didn’t realize Greyhound was an option.