I've been checking the comments and trying to match every highest score I see, today I beat one! I haven't seen anyone else get above 1680 in Size 2, and I got 1705. My strat might be different from what other people do as the improvements that let me push it over 1680 weren't too hard to figure out. Only got slide 2 and turtle 2 left to improve.
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

