Looks like a really fun quilt! I am just throwing this idea out. Would you get the same effect if you made the strip squares and then used the quarter square triangle techniqe to sew two squares together? I am thinking this might be a way to avoid the bias altogether. Spruce Crafts has a nice tutorial. I would post the link, but I am not sure that it is allowed.
I hate working with triangles. I think they get stretched out when I iron because I drag the iron instead of just placing it on the block.
Have a great day!