While doing the 12 Ides 1000 Insanity series, I found that the only thing in the town where I had to start/finish in was the post office. I took a picture of my bike in front of it and posted it to Spotwalla, as well as including it in my app. I then rode to the nearest place where I could get a receipt (which in my case, was about 100 miles away!).
So in this case, if nothing is open or can give you a receipt, take a picture of your bike at some landmark and then go to the nearest place to get that Almighty DBR.
Also: ATMs are always, in my experience, reliable, and I have used them a few times when nothing else was around.
Tim used the Venice Inn Motel for his ride last year and was able to obtain a good receipt. In his ride report he mentioned that late night the 2 motels were the only (at the time) viable options.
There is a gas station at the store on the east side off the road if you go almost to the end of 23.
IIRC Hartt's Exxon 42813 Highway 23 Venice, LA
I hope thats the one I used. I went all the way down 23 then stopped at the first one I came to.
Depending on when you get there, either the Cypress Grill or the marina restarant may be able to help you out. They are closer to the actual end of the road.