Now I have moved /var to the SSD, and at the moment things are blazing. However, as I mentioned in my original post, the problem with slow IO performance only happened sometimes, not all the time. So I don't dare to consider the problem solved just yet.

Regarding the /tmp mount point: yes, that was done manually. I wanted to move both /var and /tmp away from the SSD, to reduce the amount of writes to it. I hope putting /var back on the SSD won't kill it prematurely.