My size 2 is 1710, I can get the score with either turn-freeze or turn-all. You can go a little higher than that. But, I stopped trying to max scores with All because I found the move tactic chaotic and generally unfun.
You can also get to at least 1225 in turtle 2 using Freeze, but others have gone higher,
The maximum scores I have seen claimed (but not verified) are...
Ice 1 1360 5 boxes; Freeze
Ice 2 1430 10 boxes; Freeze,Turn
Lily 1 1240 7 boxes; Freeze
Lily 2 1680 5 boxes; All
Move 1 1300 11 boxes; Turn
Move 2 1760 6 boxes; All
Size 1 1520√√/1600 5 boxes;
Size 2 1710 9 boxes, Turn, All/Freeze
Slide 1 1600 6 boxes; All,Turn
Slide 2 1280√/1488/1600 9 boxes; All
Turtle 1 1520 7 boxes; All
Turtle 2 1360 7 boxes; All,Turn
