I'm also one who tends to bind in the same fabric as the final border.
That being said ... contrasting bindings can be very effective and dramatic.
And as you said ... a picture would help!
There's so many variables ... the tones of the colours you mentioned, the width of the sashings/borders/frames, how many blocks you have etc.
With the embroidery in the blocks, I'm thinking you probably want to pull the eye to the blocks, rather than away from ... which would be a huge consideration as to what might be done.
Perhaps tonight, you'll take some pics and show us!