I'd first go with what Opti says ... simply because those areas he identified are the first places to look. If balance/steering/suspension/brakes are out, you're chasing a ghost anyway.
Now, it's not beyond all realm of possibility that there is something in the Miata that is unique and causes some shimmy at some point. Talk about the hardtop/softop experience does suggest something is going on.
The question is what? Does putting on the hardtop fix the problem, or merely cover it up? If there is some kind of chassis/body flex that is at work, it could possibly be both, I guess.
Has anyone tried to run a rear shock tower brace to fix the problem? That should address left-right flex, at least to some extent. It does simulate, in that dimension, adding the hardtop. Might be worth a look.
Originally Posted by sakana
However, I bet there's a significant resonance in the chassis at the same frequency that an imbalanced wheel at 65mph inputs force to the chassis.
Furthermore, I bet that it is either torsional or fore-aft "bending" stiffness of the chassis that is in question. This would explain why a hardtop would solve it and a roll bar does not-- the hard top adds stiffness to the chassis front-to-back and torsionally. A roll bar, on the other hand, adds stiffness to the chassis mostly laterally (side to side.)/engineer out
I think you're absolutely correct in that it could easily be a case where fore-aft and/or torsional issues could be at fault. Most convertibles have some issues there. It seems to me since the Miata is a droptop from day one that it wouldn't be a problem, but you never know. Ragtops made during the last few years seem to address it better than 90's (or earlier) designs. Maybe they know something now they didn't before.
What about frame stiffeners under the side box sections? That should at least change the flex frequency if it's fore-and-aft, which you should be able to detect as a change in the speed that brings it about.
In either case it might point us in the right direction.
Are people using aftermarket wheels/tires/brakes and if so, what do they weigh?
Does anyone have any experience with replacing body/steering/suspension bushings? Even with just stock stuff, it might be worn to the point where it's the culprit.