You have a beige in the upper left corner of you photo and several others through the block. I would look for a beige fabric with a brown design...nothing too bold, perhaps some curliques and use that to frame each block. Browns and blues go together very well. Perhaps you could find a brown (to match the above suggested beige/brown combo) with a darker, closer to the cobalt of your walls in it to finish off the quilt. Something like a hand dyed type that goes from beige to brown to shades of blue. You can find it...just keep looking and don't (regardless of what colors you prefer to use) settle for something other than what you want. Just put the quilt away for a while and you WILL run into the perfect fabrics when you least expect it.
If you are considering what I suggested, color wise, may I also suggest that you do some fancy stitches on each block (not necessarily every strip) but use all of the colors of thread that are in the framing and finishing strips. It could make it very striking.