I do have a possible suggestion to consider that will let you use those cotton balls and renew the scent on them as well as not allow the rodents haul them away. Put the cotton into refillable tea balls. The kind you put into a teapot or tea cup. As they are mesh or made with lots of surface holes the scent will come out. Rodents can't easily chew through those stainless steel containers and they will hold up to weather as well as heat. But do secure them in place so they don't bounce around as you drive.
I think I will try it myself. Scented cotton balls in a tea ball, it certainly seems like a doable setup but of course at this point a concept rather than something I have tested. The large ones could also hold moth balls.
Perhaps tea balls are dollar store items? I have never looked for them there but it seems likely to be in the kitchen utensil area. Walmart is very likely to stock them. Nothing to fabricate, not messy to use, easy to renew the scent, low in cost, easy to find in stores, it meets the "worth a try" experiment criteria.