Josh, your not making the wisest move here based on your reasons for a 'directional tire'. You don't need a specific directional tire on an AWD vehicle like the Matrix......they have to be rotated on the same side of the car regardless.
You mentioned Safety is high on your list for your new bride, considering the winters & such.....the TT's have that in spades, much better than the Falken's do (just look at the tread designs)......if you want to 'compliment' & take full advantage of it's AWD capabilities (and stay away from winter tires in the process) the TT's are the right choice for that car without question.....I can't stress that enough bud.
I could have got the Falkens for my wife's Forester........I thought about it, but knew it was not the right play. ;)
What's the worst that can happen? In a year, if you want to upgrade to larger wheels & such you sell the TT's (very popular size) with a good amount of tread remaining & recoup some of the money invested......it's a win-win situation. :D The Falkens won't be worth anything as their tread isn't designed to last much longer than 30k miles on 55 & lowers series tires......you have an 80k mile treadlife with the TT's. ;)