Mike,
If you have to have white, maybe it would be a consideration to get the black roll up unit, then take just the fabric cover to a local upholstery shop (or boat shop as they often make custom canvas covers) and have them replicate the cover in white???
The new white cover should hide the black frame and attachment rails to maybe give you the look you want.
No idea where your "budget" is on this, but maybe a viable option.
Will also keep a look out. Good luck in your quest.
