I think it would have to be in partnership with a rideshare company. Hopefully, they would agree to offer the reduced rates in exchange for a tax deduction for charitable contribution. Also these vouchers could be purchased by family members or even groups like Autism Speaks (purchased with charitable donations through fundraising) and given to those who just cannot withstand the long wait after appointments
I feel that the citizens could be better served if that service were supplemented. I think that if there were some kind of voucher program for rideshare such as Uber or Lyft and bus passes at reduced / freecharge it would eliminate all the issues. Even if the service were to remain operational for our citizens with serious mobility issues and offer Rideshare or bus fare options to Citizens with disabilities that do not have issues cognitively or Mobility wise it could cut the wait time down for the other citizens that do have to utilize the service.
I believe and this is just speculation, that there aren't enough of the vans that do the pickups operating at one time. So if there are 10 vans operating and there are 400 people utilizing the services, then a person waiting to be picked up from their doctor's appointment would have to wait until that driver routes over to the area where they're waiting to be picked up. I believe there's just not enough funding for them to have more drivers and vans out at one given time.