You're correct, @tedmiston. With Fair, you can return your car anytime (with a 5 day notice). So, you could keep the car for 1mo, 7 weeks etc. Fair will pro-rate the last month. Fair probably doesn't make sense for folks who just need a car for a few days. Happy to field more questions here (or email me: username @fair.com)
By the way, with my referral code (SHAANR100) you can save $1,000 off the start payment until 10/31/17.
Check out Fair.com also; Los Angeles only right now but also offers no-term flexibility. There is a 'start payment' but all said and done, Fair may be cheaper than this depending on how long you keep the car.
Square seems to be the go-to AFAIK.. they probably have the widest following in terms of absolute number of businesses adopting them. I could be wrong though.
I just spoke to them on their website's livechat/Olark -- they're very responsive and helpful. Also the service is free so no reason not to play with it.