I can’t speak for others who come here to help, but I’m just a technician. Not an installer. There ARE companies out there that not only repair equipment, but install it as well. What griddles I HAVE moved were counter-top ones (not drop-ins)…and required some proper preparation for moving them…along with a small team of us to do it.
I said that to emphasize that hoisting a 300 lb. griddle out of a counter-top should probably be done by a company which does that sorta thing. Their guys would have the experience and knowledge necessary to adapt to your situation…since most any situation is unique. They would also possess whatever tools/materials necessary to accomplish it. Along with standard tools, they may have some specialty tools…along with simple stuff like lengths of 2×4 or 4×4 timbers and black pipe in order to prop the griddle up and maneuver it as necessary.
Is there a lift for doing such things? The closest thing to a lift that’s commonly used for kitchen equipment installs is a lift Genie. It’s just a hoist-operated forklift type of device. It’s HIGHLY unlikely that it could be used in your application, since it probably wouldn’t fit in your kitchen.
So the method for getting that griddle out of there will simply involve the tools/materials I previously alluded to…and the brute strength of a 2-3 man team that has enough experience to do it properly and SAFELY.
It’s more of a job for a Millright. a electrician and a tech combined. There are many fasteners that will not want to turn in the removal of the heaters and thermostats let alone the bottom pan. Bet on at least a day. Worst yet if built in. Then you also have gaskets to worry about. Cost of labor will approach a new one. Make sure you also have the right wire and crimps for high temp on hand as well as extra fasteners.