You may want to give some of the local rental places a call, your timeframe is a bit late in the season and if they are still operating, ask about a discounted rate for the extended rental. They may be willing to work a deal.
I see the idea of short-term purchase isn't ideal, but Golden Triangle Bike Rental is having a sale of used bikes on Sept, 15th. The city cruiser / commuters are listing for $169.00-$189.00, which is cheaper than renting.
Instant Plan B. Buy for cheaper than rental, use as needed, then dontate to Free Ride.
Pops gets some wheels, FR gets a healthy donation, and you get oodles of good karma.