This VERY NEARLY has only one solution. You can get VERY close to the end without any temporaries. The bottom center is a bit nebulous, but the there's a pattern established in the top squares. Makes it very easy to guess. (I'll confess, I didn't figure out the pattern until after I was done, but even brute forcing this, it was relatively straight forward.)
(I'll confess, I didn't figure out the pattern until after I was done, but even brute forcing this, it was relatively straight forward.)