How can I install craftsman-style door casing where it interferes with hinges?
The simple answer is that you adjust the reveal to accommodate your hinges. Whether you do this just on the hinge side or all the way around is up to you. It looks like you'll want to paint the jambs before installing the casing anyway, so it shouldn't be an aesthetic problem. Sand down the paint ridge a bit so it doesn't show.
It shouldn't take more than an extra 1/16&quot; to clear the hinges, and even if the casing is against the hinge you're unlikely to have problems.
I absolutely would not carve out for the hinges. This looks amateurish and sloppy, in my opinion, as though you failed to plan well.
Of course, you could always replace your hinges--modern ones tend to have smaller barrels, but I think that's unnecessary. It's also often more hassle than it sounds since screw patterns and leaf size are not standardized.