Hmmmm, the thing is the star of this quilt should be the BOM blocks, right?
If you start putting all those pieces around the edge, they're going to take away a lot of the attention from the center.
So, no, I wouldn't put the pieced squares on as another border.
And I don't want to send you off the ledge, but you did mention taking off a border.... ;-). Ripping isn't so bad. Really. And you can take this as a totally personal opinion, and please feel free to totally ignore it.
I would take a look at what the quilt would look like without that white border...perhaps a bit of the gold in it's place. I think that might make the center really pop out - which is should. Because it's the star. ;-)
Whatever you do, the blocks are lovely, and were obviously a lot of work. Was it from a pattern, or a LQS BOMC?