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Re:Show HN: Solving Rush Hour, the 6x6 Sliding Block Puzzle by djflutt3rshy on Wednesday July 11, 2018 @07:01PM (#17510916)
http://cs.ulb.ac.be/~fservais/rushhour/ has a listing of puzzles that take the most moves, but also mentions how many different configurations are possible.

The guy who made the website literally wrote his master's about it: http://code.ulb.ac.be/dbfiles/Ser2005mastersthesis.pdf

Re:Show HN: Solving Rush Hour, the 6x6 Sliding Block Puzzle by fogleman on Wednesday July 11, 2018 @07:26PM (#17511045)
I linked to this in the Prior Art section. This is the one I wasn't very impressed with. For one, his "moves" are unit-steps.