When you sew your strips together, have one outside strip with the pattern right side up, and one with the pattern upside down. That way, when you flip, they will both be right side up.
After you cut the strips, layout your block so that the opposite corners face the same way, and the other two to opposite direction. I think you will need three stip sets to get the right layout.
U x D
x z x
D x U
or
D x U
x z x
U x D
Then you would rotate the D's to make them right side up.