I have lots of experience with the 65-70 mph wiggle effect.
First, it is a combination effect of tire construction, tire pressure and rear wheel alignment.
To start your investigation, find a hill on a major road so you can go 55-60 mph and take your hands off the handle bars. You don't want to get up to the wiggle range, you just want to see how far off kilter your rear tire is tracking. The off amount you see on your front handlebars hands off is mirrored exactly on your back wheel, so adjust your back wheel to make your front handle bar error go away.
Note while doing this test, all roads have a crest to them so they shed rain better. Get up on the top of the hump to do this test stuff.
Also note how far you have to lean your body to the side to keep the bike going straight. As you get the rear end aligned better this should decrease (but never quite goes away).
Air pressure. Keep your tires fully inflated. The wiggle is a way the bike has to telling you it is time to check your air pressure.
As you get your bike tuned in better, the speed at which the wiggle occurs goes up and the severity of the wiggle goes down.
As your tire gets older the wiggle goes down. When your tire goes past the half way worn out mark, the wiggle generally disappears.
This makes me think that tire construction "variance" has something to do with the wiggle (tires have run out inside their own construction, both radial and lateral run out, both of which would contribute to the wiggle effect.
Wiggle, you live with it until you wear it off.
A bike tire only lasts a year or two, so buy you a set of Metzlers next time and jest not have these sorts of issues.