Thanks everyone! It's been a bit more brutal than previous migrations, but hopefully we'll get some much better performance as a result.
So far the server has performed even better than I'd hoped... whereas we'd normally be maxing out at around 75-85% resource usage on an average Tuesday night, this new server is barely even registering a load of 5-10%. This should translate to faster load times and fewer failed page loads for everyone. It also gives us some breathing room for adding new features down the line.