Re: Cut back, or pull out?
If the outside of the plant is still flourishing, then selective pruning to open up the canopy and let light in will probably do the trick. I would start with that and save replacement as a last resort.
You don't have to cut it back or even hack big holes into it, just carefully remove some of the perimeter foliage and branches to open up the plant a little bit without destroying the shape or size. Start slow, remove a small amount (25 - 30% ) at a time and wait for next season to prune more. This will help maintain sight-line screens and bush symmetry and the overall aesthetics of the bush.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!