"But the building is far too heavy for the jacks to actually lift it!"
Hmmmm.
First, you only have to lift half of it: 686,000,000 lbs / 2 = 343,000,000 lbs
Then you assume a typical hydraulic pressure of 10,000 psi
343,000,000 / 10,000 = 34,300 square inches
If you use a jack with a 5" diameter piston, it is 20 square inches
So you need 1715 jacks
If we assume the jack base is 1 foot square, then you can get 100 in the length of the short wall of the tower (I believe it's about 100 feet long).
1715 / 100 = 17 rows of jacks, 100 in each row
Of course, you probably would also want so in part of one of the long walls. So put jacks under 100' of THAT wall, too.
Then you only need 9 rows.
spsalso