This is thinking out of the box a bit... but you might consider doing a little bit of applique in the beige squares, using a third print, then use that for your border.
For example, applique a Shamrock or Heart shape, etc. using a blended fabric of beige and purple, or add a complimentary green as your third color, or if your existing color is medium purple then a light lavender or deeper purple might work. Don't despair... if its frustrating you... lay it aside for a day then take a fresh look at. It will come together and you will probably like the new look better than your original plan. Can you post a picture of it?
Last edited by Just Jan; 11-06-2015 at 07:12 AM.