Your extreme white fly outbreak and your proposed solution reminds me of the Tussock Moth epidemic we had in eastern Oregon/Washington during the early 1970s. The caterpillars were severely defoliating Douglas-firs and white firs in the region. It was bad. The US Forest Service panicked and aerial sprayed thousands of acres with 2,4-D. You may remember coverage in the press?
So, a state park with old growth firs growing in it, all of which were heavily infested, put the trees up for sale to timber buyers. There was an auction. The successful bidder was given three years under the contract terms to cut down the trees.
The buyer did not cut the trees the following year. They held them in reserve for when the log market might improve during the three year period.
What happened? The trees flushed out the following year! They were not dead after all. They had enough reserves to regrow their foliage.
But a contract is a contract, so the state park became a clear cut.
Moral of the story: insect infestations are on a boom/bust cycle. The worse the infestation, the sooner the insect population crashes.
Maybe this pertains to you?
If it was me, I'd wait. The hedge could maybe withstand the infestation and recover. The gamble is worth it.
Please let us know what you end up doing!