Heroes in order of first use: Thief → Bard. Pieces that end up somewhere new: the beamcaster and 2 of the 7 goblins. 23 other pieces stay where they start.
Hint 2
Start: pull the left beamcaster right 2 tiles, pull the left beamcaster down 7 tiles and pull the left beamcaster left 3 tiles.
Hint 3
Finish: pull the left beamcaster right 5 tiles, lead the 2nd bottom-right goblin from the left right 4 tiles and pull the left beamcaster right 4 tiles, then head for the exit.
Pieces that end up somewhere new: the beamcaster and all 3 blocks. 1 other piece stays where it starts.
Hint 2
Start: swap the Wizard with the bottom left block, swap the Wizard with the bottom left block and swap the Wizard with the bottom left block.
Hint 3
Finish: swap the Wizard with the bottom right beamcaster, swap the Wizard with the bottom right beamcaster and swap the Wizard with the top right block, then head for the exit.
Pieces that end up somewhere new: all 3 dragons, both blocks and all 3 beamcasters. 1 other piece stays where it starts.
Hint 2
Start: swap the Wizard with the top left beamcaster, swap the Wizard with the top block and swap the Wizard with the top beamcaster.
Hint 3
Finish: swap the Wizard with the top block, swap the Wizard with the top beamcaster and swap the Wizard with the top right beamcaster, then head for the exit.
Pieces that end up somewhere new: both beamcasters. 1 other piece stays where it starts.
Hint 2
Start: swap the Wizard with the right right beamcaster, swap the Wizard with the left right beamcaster and swap the Wizard with the left right beamcaster.
Hint 3
Finish: swap the Wizard with the left right beamcaster, swap the Wizard with the right right beamcaster and swap the Wizard with the right right beamcaster, then head for the exit.