As suggested, go to a radial tire.
The 165r15 is 25.4 inches diameter with a 6.5 inch section width so it is close to what you have now and is available in a radial which isnt prone to the dreaded flat spot of bias tires.
Bias tires flatten out under the weight and once you drive it they heat up and smooth out-a little. LOL
Also as suggested, the only way to stop this with the bias tires is to take the weight off them when not in use. The dollys wont work cause it is still sitting with weight on the tires. Sit it on jack stands.
Good luck!! Nice shop and car!! And NEVER sell your motorcycle.
