I feel like prettying your site up should only be a minor consideration when doing a redesign. You need to have clear goals, and some hypotheses on how to reach those goals. It sounds like his hypothesis was "If I make the site nicer looking, then more people will sign up and pay". By looking at the data he's found that isn't the case.

There's still a lot of other stuff to test on a site, only some relates to how it looks. Things like headlines and images/screenshots can have a huge impact. A nice design gives you a good base to work from, but shouldn't be the end. Throwing in the towel and saying "design must not matter" is the wrong way to go.

For example... their new site has way too much text, not enough visuals. Especially the features page. I would add some screenshots and try to use a more descriptive headline. Instead of "Features" or "Gory details" I'd try something like "We make WordPress run like a well oiled machine".

There's a Japanese word that represents the process perfectly, "kaizen". Committing to continuous improvement will end up in results eventually, fancy design or not. Design can definitely be part of the process, but it's not the only thing to work on.