A friend of mine had a similar problem with a channeled, fenderless '31 Ford coupe several years ago. It turned out to be simply an alignment problem. Follw Bob Parmenter's recommendations above first. If all your front end hardware checks out to be OK, try increasing the toe-in just a bit. If this changes the speed at which the shimmy starts (or eliminates the problem altogether) then you're on the right track. Most beam or tube front axles call for 1/16" to 1/8" toe-in, but if the caster is more than about 5 degrees and the car is light weight, it may require a bit more toe-in ( possibly up to 3/8" in extreme cases).