I've been cleaning griddles at work (I'm a cook) for over 25 years. It is a filthy job when done the traditional way.
A few years ago we discovered the product linked below. it is AMAZING. It is used on a hot griddle, and even baked/burnt on black stuff melts away. Really baked on stuff - let it sit a few minutes. Yet the product is safe to handle - no dangerous caustic like most commercial griddle cleaning liquids. I highly recommend it. It won't harm aluminium surfaces. You MUST use it on a hot surface. When cold it does nothing. In use it will produce some smoke, that is normal. Use your range hood.
I'd contact 3M and ask them for reps near you, then ask them if any stores/restaurants near you use the stuff, and try to buy a little of the liquid from them, so you don't have to buy the whole kit. You could use a regular scourer or buy a black 3M griddle scourer from a cleaning supplies store. (a wholesaler of cleaning supplies to restaurants or cleaners should have them.)
Traditional method uses a 3 piece kit - griddle screen on the grill surface, then a black scourer (black ones can usually take the heat) , then a metal plate with handle on top. You flood the griddle with clean vegetable oil, and use the handle and scourer stack to push the grill screen around. The griddle screen is impregnated with an abrasive which will gently grind away the baked on muck.The screen looks like a square of flywire. It is a slow and dirty process, I strongly prefer the 3M quick grill cleaner (the orange liquid.)
Just to be clear - 3M make 2 systems - the older one is griddle screen, griddle pad, metal plate with short loop handle on top - use with vegetable oil.
The newer system is orange liquid, griddle pad, and long black handle.
Do NOT use any caustic soda based product. They are VERY dangerous.
This link is the GOOD system: