Help! My brain isn't working tonight . . .
 

I'm getting ready to do my quilt sandwich. I'm using a pieced back with the pieced blocks on the outer edges so I don't want to risk the front and back not coming out the same size after quilting on my Featherweight. They are really close to equal now (less than 1/2" difference).
Is there an easy way to compensate for the possibility of things not ending up even that does not require trimming after quilting?

This risk is the reason I always used pieced blocks in the MIDDLE of the backing rather than on the edges.

It is very hard to keep a got-to-fit-perfectly backing fabric where it needs to be after quilting the sandwich. Allowing extra fabric at fall extensively along the edges of the back of your quilt will also give you room to trim and square up your quilt after it is quilted. It's pretty hard to tell if a backing does not perfectly "fit" or match the front of the quilt because you really can't see both at the same time.

Jan in VA

Thinking out loud here - can I do a border/binding that wraps around the edge via the birthing method and if it ends up wider or narrower on one side or the other then so be it?

With it being such a tight fit I thick I would take a minute & add a 2-3" border around the backing. That way you have plenty of wiggle room. I've done this before on some small quilts where I had a special fabric but not quite enough. I pressed the seams open & then after quilting just trimmed the backing.
You could even just add a strip to 2 sides (1 in each direction) and then it would look like part of the design for the back.

What if you put a small border on both sides of the quilt? I think you would find it easier if you made the back a few inches larger than the front. You could put marks on the inside of the overhanging backing to help you line up the blocks on the front. It's nearly impossible to align perfectly, but if you are careful, you might be able to come close enough. How are you basting? I think spray baste would hold it more where you want it than pin basting.

Sometimes being a quarter inch off can be more annoying than having something totally off-set on purpose.

Can you rethink your backing so you have more wiggle room?

It is really hard to get both sides lined up perfectly.

why don't you want to trim after you quilt? The easiest solution by far would be to add a narrow solid border on the backing and trim. This will also stablize the pieced edges of the backing.

I have tried lining a border around backing and it isn't easy. Most of the time it has to be what it is.

lots of pinning and taking extra care in the quilting and go slow. Pay attention to what is happening on the back as you quilt.