Don't know about hairspray on the rim, but it's certainly worth a try. Two other solutions: smearing a little silicone seal around the inside bead area of the rim may help, and one that will definitely work (we've used it on non-beadlock rims on sprint cars when absolutely necessary) drill 4-6 holes approximately equal distance around the bead area of the rim and screw sheet metal screws into the bead area of the tire. The screws should short enough to penetrate about 3/4 of the way through the bead of the tire. Brute force, but it works.
Later Addition: Don't know why I forgot this - it's the method we settled on after the sheetmetal screws above and doesn't require any alteration to the rims. Go to any well stocked hardware store and get a pack (roll? - can't remember) of the adhesive backed strip material about 1" wide that is used for sticking to stair steps to add traction. Cut pieces off the end about 1/4" - 3/8" wide and stick several of the resulting little rectangles to the inside of the bead surface of each rim. The stuff sticks really well. Worked just as well as the sheetmetal screws, was less work, especially at tire change time, and no permanent alteration to the rim.
