> Personally as a first step I would just migrate it to a better, dedicated server. Consider the cost of your time to research it.

I strongly believe that's a terrible idea as the first step. It may be a solution once you know the reason for the slowdown, but if it's something trivial like a lack of database index, or an accidentally quadradic algorithm, you'll just run into the same issue on a bigger host in a few days with more traffic.