Hey, Mr. Paul, don't know it this is your problem or not, but over the years of riding and working on bikes, I have found that, especially, on older or high mileage machines this fact. A wheel and/or tire even slightly out of balance or out of round can cause the shimmy. You see a spinning wheel will go thru "harmonic" balance and unbalance at certain rpm's. when the unbalance cycle is present the forks tend to flex fore and aft, on both sides, alternating side to side very rapidly. The results is wheel shimmy. If you were to continue to accelerate pass 40 to 45 mph, at some point the shimmy would return and be more pronounced. I hope this makes sense to you. Your thoughts please.