Have you tried to crochet that second square with the same hook as the first square? Sometimes just because you change yarns does not mean that you have to change hook sizes even if the manufacturers gauge on the band says so.
Is it really that big of a difference (which is actually quite a lot) that you lose a whole round of dc's?
It's helpful but not set in concrete that you should be able to seam with the same amount of stitches for each square. Maybe you can have it be a design feature where you have the squares with big yarn as the center and have the smaller squares on the outside. Sorta like sashing on a quilt. Or have one fat strip of squares and one skinny strip and sew them together, and if there's a big difference between the length of the two you could make that up with some dc rows going back n forth on the ends of the shorter strip.