Having glanced at this, it seems given all the circumstances that the most elegant answer would be to deepen the rebates. However - it'll be a task to do this neatly. People are swift to shout 'router!' because they like their toys, but you'll have to work out how you are going to control that router - the router fence riding against the moulded architrave isn't a terribly stable solution, especially at the corners.
Maybe think in terms of temporarily screwing on a planed, straight guide batten or two, if there's room. That'll only leave some little holes to fill later. Overhead will be the fun part! And the corners would be finished with a sharp chisel & a mallet. All in all it's a simple operation that needs a good level of skill! If you lack confidence, either tough it out and learn on the job, or pay a craftsman to do it ...