Hey MrsO, Welcome!
to address your question, let me pose one, why not just rip the door in half, right down the middle? I think that would look fine, and would only eat up 1/8" of wood.
If that is not acceptable try using a router table, or make one your self with a piece of plywood. You can make your own table with a piece of plywood and a drill. Drill a hole for your bit, (use a bearing bit), and drill and counter sink the holes for your bolts to attach the motor housing to. You will remove your router base for this. Some recommend installing a pin, or small diameter post just a few inches from the bit to allow you some control. Anyway, this will keep everything square with no tipping of the bit and your work should come out beautiful! Of course by all means run a few samples thru to get the feel and be sure your happy with the bit height.
He is no fool who gives what he cannot keep to gain what he cannot lose
If you cannot stand behind our troops, (and I understand, no judgement here), then please stand in front of them, remember, they're willing to stand in front of you!