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No way would I build up the walls an extra 1".
Option 1: recessed 1" timber strip behind the architrave to make a big shadow gap (not very shadowy). How much depth is there? At least 1/2" recess would look ok.
Option 2: add hardwood strip all around the architrave, mitred corners, paint to match. You don't want the front faces flush as the join will look annoying so either push it back or make it stick slightly further out. It will just look like part of the architrave.
The old boxes were 5" deep because the original single glazed sashes were that way. The replacement double glazed PVC was also 5" deep because they didn't have any sashes, only tilt windows.
The new ones are a full 6" deep and they can't sit any further out of the house so they're in the same exterior position which means they protrude into the room by 1".