ok, sounds like two quilts it is...now are you asking us, what we think you should do about border, OR, what we would do, lol?
I would put some applique on big block outer border. The scrappy log wosit, is great as is, needing it's quilting of course. :D
P.S. don't mind me, I would applique the world, if it would hold still. :wink: