I just replaced my worn blinds and had the same issue. My answer was two steps. 1) ordered 6 sets of cellular blinds from Blindsgalore.com for $400 Kids complained of the cold draft in the winter so wanted more insulation. 2) go to Lowes and buy a foot-long flexible shaft for your power screw driver. Remove the screws on old brackets. Use the same holes to mount the new brackets.

Ok, step 3. Marvel at your luck that the process actually works and stuff fits.