NMP is a solvent that would probably work. All these softeners will weaken and eventually destroy a tire. But it takes time to penetrate the rubber. You do not want to get them near the tire cords. NMP is relatively environmentally friendly. It is an ingredient is some paint strippers. Heat will greatly accelerate the absorption of any softener (solvent, plasticizer, same thing) into rubber.
NMP = N-methylpyrolidone, boiling point 400F