Need to soften vinyl

My tank bra is getting pretty stiff. The stiffness wouldn't matter except that the edges by the gas cap have set in a curl from wind lifting them up/some gas spillage etc. The tank is off for the winter so I can give the bra a good cleaning and months of soak with a softener. Any suggestions for softening vinyl other than Armour All?

I've used this on vinyl car seats with good luck.

www.meguiars.com/?vinyl-rubber-plastic-p...yl-Rubber-Protectant