A catalytic converter can be "overwhelmed" by excess oil and the resulting ash and soot, and once coated, rendering them useless, but not always "burnt out".
If the engine is now at proper mixture, I would think that extended, hot (high RPM) freeway runs might burn some of the old stuff out enough for the catalyst material to finish the job itself.
I've seen gas additive cat cleaner on the JCWhitney site....Snake oil??
Some commercial cats are cleaned by heating in a kiln for 2-3 hrs, at 1050 *F. (I've done similar to this with chem. laboratory grade catalysts).
A technique that I read somewhere? (heavy eqipment site??) involved removing the cat, using Superconcentrate Gunk solution to soak the core for an hour (repeating as needed), rinsing with hot water and finally drying with compressed air. I don't know if this was on a metal foil or a ceramic substrate catalyst, though.
Most cats that are run with excess volatile HCs (propane, gasoline) for an extended period of time, burn up due to the higher than designed heat of reaction and are best replaced.
The Golden Rule
1984 300SD (bought new, sold it in 1988, bought it back 13 yrs. later)