Alan, a skinnier street tire might be a benefit during Drag Week if you encounter a rainstorm. Less chance of hydroplaning. I would just consider them a Drag Week only tire, like my BF Goodrich tires that I use on my Mach. Since they're going to see very limited use, maybe just buy a cheap set?
I'm at a loss for what to do with my Galaxie. I don't want to buy drag tires for a car that will likely never see the drag strip again. But according to the rules, you have to have a dedicated set of racing tires

Heck, my car probably won't even do a burnout unless it's on 1 tire alone

I'm not sure what to do, or what I'm going to do, but I know I've got to figure it out quick!