It could also be that the front fork is out of alignment. If your front wheel is sits to more to one side than the other, lets say to the left, and you flip it around so the tread is opposite, and the wheel still sits to the left it is your fork that needs to be realigned, if your wheel ends up too far to the right when you flip it around, the wheel is likely dished (trued out of center) and is still not tracking in line with the rear wheel) causing a shimmy.
I have a protovelo that I had crashed, which the fork ended up, and may still be slightly out of alignment. I was having a major shimmy with no hands, dangerous i would say! Once I identified the problem using the wheel flipping technique, I found a solution on Sheldon Brown's website, which basically says to lay a towel or piece of cardboard on the ground and lay bike on top. With the front wheel removed, hold the the side of the fork in your hand that you would like to adjust and brace the opposing fork blade with a soft rubber surface, such as your shoe. Pull blade of fork in the correcting direction, repeat until wheel sits centered, LOL. Hey, it worked for me, albeit taking all the strength I had and a fair amount of patience.
I think some LBS also have a fork alignment tool that will accomplish this same task if not feeling up to being a brute.
Best of luck,
MIke