So very pretty -- not nearly as bad as i was picturing--- seeing it, i'd say yes - stabilize the blocks - perhaps with a light to medium weight fusible stabilizer - you might even be able to do it without taking the blocks apart - cut the stabilizer squares - slightly smaller then current blocks - iron to back side of each - re-stitch with slightly larger seam allowance to catch the stabilizer - then quilt. Anyway - -just a thought -- you'd know best if that's doable or not. Again - GOOD LUCK !!!