I don't see why it's important to have it match up. No one will care but if it is super important to you then sew the border on the backing either by applique or machine then quilt the quilt.

Well it sounds like most replies say nix this idea. If it was my stubborn self I would try anyway. Just cut your backing border wider as paperprincess suggested and trim the excess after quilting. You don't want the top and bottom at exactly the same size when you sandwich it. Getting it to match perfectly will drive you crazy

If you are determined, then I would cut the back as big as the yellow border you have already added to the front. That allows for some slippage. Make your batting at least an inch or two wider than the front yellow outside border. Pin or spray glue everything really good. You want to keep everything as stationary as possible. Then quilt from the center out stopping before you get on the outside yellow border. Now, add the last yellow border by folding down the front yellow border, pinning the new border on the back, then sew on the original seam line. You will have probably have to unsew at the corners on the front to get the new back strips on there. You'll have to figure that out as you come to it. Do make sure your batting does not get caught up in the new seams. Then, fold both the yellow borders out and press them. Pin or spray baste, then quilt the borders like you want to, trim up the quilt and add the binding. I can't wait to see how you do with this. It's definitely doable, just a bit challenging.

Edited to add: I would NEVER add that back yellow border and expect them to be the same after quilting. Maybe if you are quilting on a longarm, it might work, but it would drive you nuts trying to keep them even and not get all kinds of extra tucks in the backing material.