Sorry about the post and run.
OK. Essentially, you're working with a 36 patch block. So to keep that grid, if you did a 9 patch, each of the patches would be 6" square. That's a big "splotch" and would overpower, I think, your ribbons (which are supposed to be the stars in the quilt, right?).
Also, you said you wanted to use the strips you've already cut, which makes perfect sense.
Here's two versions of using a scrappy block for the alternate in your quilt layout.
The first is a 36 patch scrappy. It's okay, but at some edges it butts up against the ribbon, and that really bugs me. :roll: I don't why, but it does.
The next pic uses 25 patch, using your cut strips, but surrounds the block with a 1.5" (finished) strip of the white. That does a couple of things. First it won't touch the ribbon (see above). And secondly, you can make it a bit bigger and then trim the block down to exactly 18.5", as you mentioned you were still a little unsure of getting a perfect 1/4" seam. Nothing wrong with that. I do it all the time. And in the end, your blocks will go together much easier.
I tried it with a 16 patch surrounded by white but it wasn't symmetrical - and I'm in a particularly anal mood, so that also was bugging me.
As you can see, I also only used 5 ribbon blocks because of the symmetry - but that's just me. You do what you want.
This quilt, with a 1" white border and 3" pink border, measures 62" square.
Wait, the pictures aren't working. I'll put them in another post.