That is a beautiful quilt - I love those skinny borders, they give a stained glass effect.
I've been doing them with a 3/4" strip and sometimes get a bit 'close to the edge'. The last ones I did, I cut them at 7/8" then lined up the left toe of my foot (which is 3/8" wide) on the inside of the seam line. This seamed to work too. If necessary, I trimmed a bit off the seam allowance afterwards. :-D