my heavily stained pizza stone

I am in the camp of scraping the stone and not worrying about the appearance.

Gerhard

I always cover the baking stone with foil when baking pie or anything that is likely to bubble over.

Documentation included and/or website info?

What kind of stone(material, thickness, etc).

Most effective is ultra high heat(oven self cleaning cycle, after scraping), but some stones may not be able to stand up to this. So not at all suggesting to do such, for maybe several reasons.

The next suggestion is to leave it in the oven at the maximum (dial)temperature. Typically 500º to 550º F or so, for one to two hours. Again, your risk. I say this because I wonder if my first thin "pizza stone" could have withstood this, over time. A "quality" stone should, I would think.

Those are the methods directed for maintaining my cordierite stone.

a good stone like a good baking pan has a baked on patina.  It may look hokey bur when your stone is "bronzed" you won't hae to do more than brush off the non-sugar residue.  YMHO

I just got a great stone from Old Stone Oven through Amazon. $39. US! Great stone and lots of room.

The only time I worry about the looks of my baking stones are when they are new.  After they get broken in I don't care how they look.  Most debris can be scraped off once it dries off sufficiently.  I also use a tinfoil sheet when baking something that might boil over but mostly mine get used for baking breads.

Actually, the "filth" on your pizza stone is what you're trying to achieve.  It's not unlike seasoning a cast-iron pan.  When the stone has cooled, run hot water over it and rub it with the flat of your hand.  Use a plastic scraper to remove any stuck-on bits, but keep rubbing under water as hot as you can comfortably stand.  When it feels like you've gotten all the surface oiliness off, dry the stone and store for the next use.  Don't use soap or detergent - it can leave off flavors behind in the stone.  The next "dirty" spot may or may not land in the same place, but eventually over time all those spots will overlap and give the stone a smooth shiny patina.  This coating is almost nonstick for most applications (except for really gooey sugary doughs, like cookies).  Depending upon how much you bake it may take a long time to fully coat the stone - it took me about 2 years - but it's worth it.  It really makes the stone a pleasure to work with.  

You didn't mention specifically what you were working with, but pizza stones appear to me to have a slightly denser, smoother grain than the large rectangular stones designed to stay in the oven all the time (perhaps others can comment on this observation).  And my largest pizza stone is a 15-inch circle I got from Pampered Chef years ago, so it fits easily in the sink for the procedure I mentioned above.  The more porous nature and greater size of the big stones would make that type of care more difficult, so a stiff brush and/or scraper may be the only way to go.

A lot of people leave the stone in the oven  through a clean cycle but having repaired enough "self cleaning" ovens I don't recommend it - it shortens the useful life of the oven (i.e. expensive electronic controls replacement $$$). 

The stone I've been using for the last several years has been sanded once - literature that came with the stone recommended using a belt sander to clean any built up "crusty" stuff. Next time use foil or baking parchment.

As far as the stone having that used looked I recommend looking up the Japanese term "Wabi Sabi" - in western culture we say that it adds character...,

Wild-Yeast

I haven't had the experience yet of ruining a self-cleaning oven. So, naive as I may be, I run the clean cycle whenever my stone starts looking a little too gross. The sugary mess from your apple pies will create lots of smoke, but it shouldn't be too much of a problem. The self-clean cycle is also great for stripping off old gunk from well-abused cast iron cookware, so that it can be re-seasoned. Same warning applies about some cast iron wares not being able to take the heat, but mine have always been just fine.

Interestingly, some people seem to have enough confidence in the oven's ability to take its own heat, that they go so far as to cut off the lock, and use the clean cycle for baking pizzas. Look it up in the search box, upper right corner of the page.

I have a Fibrament stone and it's had stuff spill and burn on it.  I wait until it's baked a bit and then when the oven and stone are cold, lay down some moist paper towels to catch the residue and scrub at the bits with a wire brush.  Then brush the dust onto the paper towels. 

i use a Lisle 52400 fold-up scraper i got on amazon. it takes single edge razor blades, and easily removes anything crusty instantly.  the "fold-up" part lets me rotate the blade into the handle so it can live safely in a drawer, without my having to learn to count in base 9.

it also is great for cleaning the wood pizza peels i use - one side for sliding the pizza, and the other for cutting the cooked pizza. in 30 seconds all the crud's gone, and it's as smooth as my bald spot. water isn't needed. 

i also use it cleaning my stone counters when stuff gets caked on hard. probably the best eight or so bucks i've spent in a long time.