I would experiment with spray starching the triangles before you sew them together. Starching stabilizes fabric so bias edges are less likely to distort when you machine sew them together. There are some tricks to using starch, though, and depending on the quality of the fabric spray starching may cause the pieces to shrink (thus distorting them).
Honestly, since the triangles are already cut out, I think this would make a good hand piecing project. It's much easier to avoid stretching bias edges and make joins meet with hand piecing, and you wouldn't have to spray starch. Jinny Beyer has a DVD out that demonstrates her method of hand piecing (which is very fast). Also, there are a couple of HGTV Simply Quilts excerpts of her demo'ing hand quilting. I posted the link to the HGTV videos in another thread. I can find them and repost here if you are interested.