Another way out is the Cunning Wish that Matt promoted above, by the way. With Cunning Wish, you can grab the bounce you need just before you win, although that doesn't help much against suppressed Fetchlands. You'll have to bite the bullet and just pay for the fetch ability.
Try to focus on a build with Cunnings.
You have more blue and a lot of islands and some duals.
You don't need red or black to win soon, you can easily wait a bit and dig into the deck until you draw Undergrounds and Volcanics.
All the engine and the solutions to problems are almost blue.
Retrospectively speaking, playing with 2-3 Cunnings, you can easily drop down to4 the fetchlands, losing really few on
tempo when facing Suppressed Field.
On a minor point, fetchlands#1 is usually faster to break when compared with resolving Suppressed Field #1. It all comes down to flip coin. You can have a free-search effect or not, regardeless which configuration you are going to play.
As an aside, I find the storm requirement on Brain Freeze quite taxing, more than the black mana on Tendrils. How is your experience? Do you fizzle more often than with Tendrils, and how much setup energy goes into a Brain Freeze kill?
Killing with Brainfreeze is a quantitatively more difficult than killing with ToA, but qualitatively really simpler.
To avoid frequent fizzles, I add to my sideboard free spells such as Gush and bouncers such as Rebuild.
The plan usually involve a good combinations of drawers and Y Will.
Gifts is "THE Y. Will enhancer" and, supported by all my 10-mana accelerators, I cannot be able to deck my opponent only a couple of times ( compared to 10-15 Brainfreeze kils ).
I found playing the two blue spells ( Cunning + Brainfreeze ) to be far more simpler than playing the red and the black one.
Even if both of the killing methods usually involve resolving an huge Y Will, I found really interesting to have two kills that can attack the opponent from two different sides: his life points AND his cards.
Playing against good opponents ( the ones who play with the blue cards and some drawers ) isn't unusual to win with brainfreeze with only 10-12 spells, an amount of spells comparable to the one needed to kill men with ToA.
More than they draw and dig for solution, more you can slow down the game, refill your hand with good spells, rearrange you godly hand and win.
....Sometimes I lost to Life.dec.. now it cannot be possible anymore...

Maxx