"except while" is correct and usable in written English.
You can use it to set apart an exception or contrast within a sentence. For example: "I usually like going to the beach, except while it's raining."
I can think he's great except while looking at his pictures.
And it was largely true – except while they were happily married, he was having affair after affair.
Near the end of her life, dressed in her then-outdated French clothing, she was rarely seen in public, except while out collecting her rents.
The paintings make no sense except while we play along, responding to passages in what the art historian Meyer Schapiro called "a random flow of private and incommunicable associations".
By Berton Roueché The New Yorker, July 26 , 1947P. 16 Incidental Intelligence: There's a sign on the railroad station at East Hamptons "Carriages Must Not Stand On this Platform Except While Actually Loading or Unloading Passengers".
In Greenwald's view, every moment a woman is anywhere other than her apartment — a place where she should spend as little time as possible, except while updating her online profile — is an opportunity to meet men.
Except, for a while, Mariano Rivera bobbleheads.
Except after a while I realised I didn't enjoy the acting".
He was businesslike all the while, except for a moment by his locker.
Color is out of the picture for a while, except for black, white and gray.
Except for a while we encouraged those people who weren't respectful of the theater as a temple.
