Front tire shimmy

To the "Brain Trust"
Our first flight is this week after 13+ years. During a taxi test we had a violent nose wheel shake that may have abort our take off if and when that happens. After checking the side drag which is at 35# we realized that the tire had a huge flat spot in the tire. It was at least 1/4" maybe more. The plane has been on these tire for over 3 years which I'm sure is the problem, and have not been balanced.
Question:
1.Run the tire anyway and hope the flat spot goes away with a few landings.
2. Replace the tire. If replacing the tire, what tires are recommended?

Rubber doesn't typically take a full set unless dried out. I would leave the tire with the flat spot somewhere other than ground contact and crank the pressure to it's maximum, then check in a couple of days. I have had a few cars that would exhibit light tire vibrations for the first couple of miles after sitting for an extended period. Always went away.

Larry