I'm surprised that nobody mentioned installing tubes, preferably a size smaller than recommended. That does defeat the purpose of having lightweight front tires, but it would be the most effective fix. I use to "paint" the insides of my slicks with dish soap, but haven't needed to with Hoosier radial slicks. Never did the fronts, but I'd be careful. Obviously, age even without sun exposure causes rubber to deteriorate. I had a "brand new" 7 year old trailer tire, stored indoors, peel like a banana after less than 2,000 miles.

(Is there a metal valve stem rule for front wheels/tires?)