Surgery can be used (as mentioned above) as a last resort to relieve persistent vertigo and dizziness, but it's very risky in terms of preserving remaining hearing, can cause total deafness.
Yes indeed. I happen to only know about the surgery because the first American to go to space in the Mercury program, Alan Shepard, was diagnosed with Ménière's in 1964, after his historic first flight, and was grounded. He opted for what was then very experimental surgery. For him it was successful and he went on to command Apollo 14, the 3rd moon landing.
