Hi, Wiley, I was thinking more along the lines of a rabbeted board, a face behind the face, that would create a situation where the relief that you choose in the hinge is accomodated for. For example, if you get a 3/4" overlay hinge, it would mount with a 3/4" overlay plus a little bit into the inset part of the door. That would give you enough room to prevent binding. You would lose about 3/4" of opening, but the inset board could be rabbeted to the back of the face frame (or all the way to the inside of the case) to make sure it's rigid.
That would be cheap and use the common compact style of hinge rather than the type that mounts to the side of the cabinet.
One obvious benefit of the soft close hinges (I have full solid raised panel doors on my cabinets, and my wife is a rough slammer of doors - I was concerned that she may ultimately lever the face frame loose from the case over time) is that users learn not to slam doors because they don't even have to close them the whole way. I think a part rabbeted to the face frame back from the original frame by about 3/8" plus a little bit would be plenty rigid.