In a smaller town you may have better luck arranging a private driver.

I would discuss it with your Uber/Lyft driver and also see what livery options are available. Gig drivers only get about 1/2 of the fare despite being private contractors, and arraigning to just call a responsible driver when you need it (or have them pre-scheduled) will result in better reliability and cost over time, since you are not at the will of the app and the driver can pre-plan to be there.