I would definitely sew strips. Cut all three of your fabrics into strips 6" wide, your FQ polkadots, and your white and black.
Fabrics
C = (color) Dot
W = White
B = Black
strip set 1 CWC
strip set 2 WBW
Sub cut that into 6" strips & sew your 9P together:
CWC (strip set 1)
WBW (strip set 2)
CWC (strip set 1)
Then cut your 9P in half vertically & horizontally exactly in the middle.
Arrange your blocks according to your plan.
(I know you know all this, but newbies sometimes wonder...)