A quick update to this: the upgrade freed up enough RAM for me to finally enable a php opcode cache. You should see no change other than faster pageloads, but if you see any new weirdness or errors let me know.
Yeah, Drupal's a bit on the sluggish side. We also have a decently big database and site relative to our budget, so a lot's crammed onto a relatively small VPS.
All done. Got a bit of a late start and took a bit longer than I'd hoped, but it shouldn't be slow anymore (after a bit of an initial warmup for the next few minutes)
Well, we've managed to outgrow the server again and need to upgrade our plan a notch. Unfortunately, this does involve some downtime. I'll be doing the upgrade Sunday night, 8PM PDT (4AM Monday UTC). The host estimates that moving will only take 12 minutes (for a total of around 15 minutes of...