I think the stay stiching might come in handy after all the pieces are together in the band you're making.
Essentially, if you were to trim the bottom and top of the band straight, you'd have the whole edge be on the bias.
That's where I might mark or eye the 1/4" seam line, and stay stich about 1/8" from where I'd be cutting the straight edge. The stitching will be hidden in the seam allowance.