You've got a really nice quilt there!
I see a solid black border about twice the width of the solid black sashing on the inner section.
Next would be a very narrow red strip, done as a flange.
Then finish off with solid black again, 3 or 4 times the width of the sashing. Bind in the same black.
This way the red strip will just gently float in as part of the border, yet provide some punch while not detracting from the overall focus of the main part of the quilt.