1973 Dodge Dart sport speed related shimmy

I believe there are 4 places that your problem can originate; the front end, the rear, the powertrain and the body itself. You have already eliminated the engine and most of the tranny by putting it into neutral at speed. So heres what I would do; get the rear wheels up off the ground, run the speedo up into the vibration zone for several minutes. Make sure not to have anything of value behind the tires in case they throw stones. Watch the wheels for wobbles or excessive runouts. Now,if the problem fails to show, it probably originates elsewhere, or in the wheels. If however, it does show we are on the right track. First eliminate the wheel assys by removing them, and securing the drums appropriately, and retest.Still vibrating? Check the driveshaft for runout or odd behaviour at the ends.Next remove the drums and retest.All good? Well theres nothing left but the rear end itself and the trans outputshaft which has only a few rotating parts on it (when in neutral). I suspect that if the problem originates in the rear, that when the wheels came off the problem went away. If so; it could be axleflange runout,rimhole to pilot runout or wheel runout. If however no vibration occured at all then we have eliminated the rear as a source. Next I would put the front wheel assys onto the rear and retest, again looking for runouts.If good then only the body and the front end are left. The body is usually not a problem but can be excited by problems in the wheels, the shocks or various suspension mounting points. And that takes us back to my previous post, which details the most common issues, esp mtg points. Also note that wheels can be fully balanced on the machine yet have enough runout(vertical hop) to excite the body through the suspension parts. Hope this is of some help. And finally I think it bears repeating;I have seen front wheel shimmies caused by incorrect allignments and loose mounting points, often. I would also check/adjust the sectorshaft end play.