Kind of ties into a current event here...
Re the suggestion to place this cookware into a self-cleaning oven, where it might be too hot and damage it. This past weekend in San Diego, the Navy ship Bonhomme Richard caught on fire. It took the weekend to put it out. In some places, maybe some parts of the ship became hotter than a SC oven. The ship is now heavily damaged, it may even be "totalled".
It turns out that many parts of the BR, like some other military ships, are made of aluminum. The aluminum not only melted, it caught on fire! These parts collapsed and so must have been exposed to a lot of heat.
Knowing this, I would not take a chance with the Guardian Service cookware. I would try using a plumbers propane torch if the crusting bothers you, but use it sparingly just enough to burn it off (if it does) and go on to the next area. Perhaps polishing it will de-emphasize the grime.
Can a SC oven be inaccurate on its self clean mode the way a regular oven can be inaccurate when baking? There's another thread about an oven 28 degrees hotter than the dial shows. Just turn it down when baking but self clean it could be the difference between 900 and 1000 degrees F.