You've already gotten the best advice. Another option would be to take the door frame moldings you intended to use to any place with a table saw and get them to clamp a "sacrificial fence" onto the fence of their table saw.
A sacrificial fence is nothing more than a piece of wood that you can wreck by moving the fence so close to the table saw blade that the blade cuts slightly into the sacrificial fence.
With the sacrificial fence in place, run the door frame moldings through their table saw to cut a 1/8 inch deep "rabbet" into the back of the door frame moldings to accomodate the increased thickness of the wall.
That way, you can nail the door frame moldings on normally, and the rabbet on the back of those moldings will accomodate the increased thickness of the wall.
(in solidarity with the freedom seeking people on the streets of Iran)