My 87 560 SEL had similar issues, smooth to 60mph, then shook like mad util 80mph, then smooth again to 100mph. I had newer Michelin X-One's on it. I had them balanced, and the shake moved to a different speed randge. Balanced again, and they were completely fine.
I agree with the other poster, certainly could be a Michelin thing. But I also have heard the pre-1995 W140's have some suspension problems from the factory. Some searches might reveal some more info about this.
2014 Tesla Model S (320 miles)
1999 S500 Grand Edition 164k
1992 300D 2.5 Turbo 287k
2005 E320 4MATIC wagon
1991 Alfa Romeo 164L 99k (sleeping for a while)
Then: 96 Lincoln TC, 93 Lincoln TC, 87 560 SEL, 87 300 SDL, 80 300D, 89 560 SEC