I have actually done what you did, had a finished quilt I just didn't like the center of, cut it out/ replaced it. The way I did it was..... Created a new center, quilted and trimmed/ squared up to fit perfectly. Then I made ( sashing strips--like binding, 2" wide, folded in half, pressed) for both sides, top & back. I lined up the raw edges, top & bottom, lots of pins, and machine stitched them like a binding to the new center section. Them I fit the center back into the hole flipped the ( binding) over and stitched it to the outer frame of the quilt. I did one side at a time, the back first, making sure the front stayed out of my way, then brought the front strips over & stitched it down, covering the stitching from the back. It turned out great, although quite labor intensive. I was much happier with the ( new) quilt