I would take out the basting sewing the rows together but leave the basting between the original blocks in the row. Then stitch the blocks in each row together with a normal stitch length. The long machine basting stitch will not hold the quilt together through normal use.
However, I'm confused by the fact that it is taking so long to remove the machine basted stitches. If they are basting stitches, they should be pretty big and should come out quickly. Cut every 4th or 5th stitch and then pull on the thread on the other side - should just come right out.