I decided to just suck it up and finish with my original plan for this scrappy tile border. Thanks for all your suggestions. I no longer totally hate it. Maybe 6 of 10. My issues is that I just don't like scrappy. Even when it's monochromatic. I was trying to push outside my comfort zone in the hopes it would add some texture and weight to the border to anchor the applique.
Next step = hand quilting. I am going to use a silk batting that I've been saving for some special reason. I'm still a little iffy on what design I'm going to use in the very center. I've been reading up on silk batting, and am not sure if I'll get the same shrinkage texture as with cotton. (They both claim 5% shrink). Anyone with experience w/ silk batting? I'm open to advice.