I would use a hacksaw blade to cut a 1/16" or so kerf at the top and bottom of the hinge location and then use a chisel or file to remove the material between.

I'm faced with the same problem NOW. How did you inset the hinges, or did you plane the doors?

It would help to see a picture or at least the brand and model of the hinges you are using.I have installed thousands of hinges and cabinet doors and am sure you are just using the wrong hinges for your application or not following the manufactures instructions.There is no such thing as standard hinges and the term partial inset is confusing although I think I know what you are reffering to.

Here's a picture of the cabinet and hinge. Because I am using different hinges (previous hinges attached to face of cabinet frame), the doors are slightly wider. Ok for single door, but I have nine sets of double doors. Thinking I need to mortise (?) the 36 hinges so that they are flush on cabinet frame. This is all new to me, so hope I'm describing correctly. Appreciate the help very much.