I haven't spent the time to build the change of basis matrix yet, but I did create two matrices representing the 14 basis vectors corresponding to each scramble. I have to run, but if someone else would like to input this into some program (mathematica, matlab), and do the necessary row reductions, feel free. If not, I'll do it sometime soon. I also figured it would be worth it to post this now in case anyone detected an error that I did not catch.
The matrices:
http://i.imgur.com/uFNwu0s.jpg
The key is hard to decipher, so here's what I used:
Corners (corresponding to front center): UL = 1, UR = 2, DL = 3, DR = 4
Front: U = 5, L = 6, C = 7, R = 8, D = 9
Back: U = 10, L = 11, C = 12, R = 13, D = 14
All numbers are indicating the direction they would go as if you faced that side (except for corners on the back, as they had to be oriented to one side). Also, the large 0s are block matrices of all 0s of the appropriate size.
EDIT: already noticed an error, the UUUU column should be all 1s, no -1s