Argh! Like we don't have anything else to do with precious spring hours but to figure out how to right these drunken sailors?
To be fair, it's not the trees' fault. Planted as a double row for more immediate screening, then allowed to grow up and up, it was inevitable that the foliage on the inside of the hedge would be shaded out. Now, when snow falls or ice coats the branches the weight's all to one side. No sway there, just a lean.
We've shown you this problem as it can occur within a single plant with multiple trunks, in What's Coming Up 204.
There, we cut back or remove the extra limbs so the single trunk can do what comes naturally -- lean to the left, then to the right, and come back to upright.
In this hedge removing trunks is not an answer. Even if each tree was reduced to one trunk and overhanging trees were pruned to give the hedge more light, the trees would remain one-sided. The leafless wood in the interior has lost the ability to sprout new leafy branches.
Staking, as you can see, is useless.
There's putting up a fence. That's against building code in this location.
Starting over with a new hedge? Even aside from being a job too big to be tackled right now, this area is much shadier than it was back in the early days of this hedge. As the hedge grew, so did trees grow to the south and west. Beginning again would mean a switch to more shade-tolerant plants, such as yews. Tall yews are not nearly so available at garden centers as arborvitaes.
That leaves bracing the plants, one of two ways.
One way is to set very tall, heavy forked branches (such as limbs removed from other arborvitaes) to buttress the outside of each arb.
The other is to lash opposing arb trunks together, using wide, strong material like seat belt straps in open loops around the wood to minimize chafing and prevent any girdling of the trunks. We'd link each pair of trees at several places, from 6 feet on up.
Ugh! We'd rather dig dandelions. From a rock garden.
...to putting this off until we can hire an under-gardener!