Strength of Snow in 6 minutes strikes me as a slightly improbable time unless you have some kind of speed boost like a Birthday Cupcake. A more realistic time is probably about 8 minutes, +-30 seconds.
Straight to the Heart can be done in 10 minutes without breaking a sweat if you play really conservatively, and it takes you 8-9 if you do it as efficiently as possible.
Realistically speaking you shave time from the Straight from the Heart run like so:
These are the groups you take, in this order
1) Glimmering Snowman + Snowmen Group
2) Snowmen Group
3) 2 x Mischievous Snowman -> 3 x Grumpy Snowmen, 4x Impeccable Snowmen (Group 1, Line)), Impeccable Snowmen (Group 2, Semi-Circle)
4) 2 x Bustling Snowmen + 1x Industrious Snowmen -> Bustling Snowmen + Industrious Snowmen (corridor) -> 2 x Bustling Snowmen + 1 Industrious Snowman (against right wall) -> 2 x Roguish Snowmen
4a) You do not have to take the snowmen over the left bridge
5) Mischievous Snowmen + Playful Snowmen -> pick up reinforcements by moas -> Blessed Snowmen
6) 2x Blessed Snowmen (Door) -> pick up reinforcements by moas
7) 4 x Cordial Snowmen (in front of traps) -> Cordial Snowmen (beyond traps) -> Angry Snowman
8) Semi-Circle of Pious Snowmen (you can skip most of this part by hugging the left wall and killing 2-3 snowmen, saves you probably a minute)
9) Kill Freezie and his 4 x 3 Columns of Snowmen, engage them from the right with your reinforcements
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