1997 Cadillac Deville Stiff shift handle

Disconnect the cable at the trans end, and see if it frees up. Has there been any trans service requiring the upper valve body or side removed prior to this?

Probabilities include something in the column(it is not a concours?), A cable that is bent/broken or fraying inside the casing, or something binding the manual shaft/valve in the trans. You do not need to get under it to disconnect the cable at the trans. The cable comes across the engine, is retained in a bracket at the trans, and the level can be seen from the engine compartment. This can eliminate the most expensive part(trans).