I'm making 120 log cabin squares at the moment and posted this same question earlier. I ended up strip piecing the squares, then trimming them after every "log" added. It takes longer, but I don't have the frustration of uneven logs and squares. I am amazed at how wonky the squares become even when being super careful. The method I'm doing now is great for me and even though some of the logs aren't exactly 1 inch (I'm doing 1.5 inch strips too), it is unnoticable to anyone but me.
Trim as you go to keep your squares square.