Here are a couple of things I would try...
:arrow: Variegated thread
I would try a black/gray/white or dark red/gray/white. Bring the quilt top along with you and pull out a healthy arms-length section of thread and see how it look against everything if possible.
:arrow: Gray thread
While it will not blend in completely, you might be surprised how it does not stick out.
And I would use the same thread in the top and bottom, unless you are confident in adjusting tension.
No matter what I am sure the quilt will be wonderful