Please understand that those kinds of evaluations are often somewhat subjective, and I was not intending to disparage your choice of platform - I was only meaning to share my experience, and yours may well vary.
My objective reasons for changing had to do with the slow development pace of PHPWebsite, the lack of activity and readily available help on its forums, the lack of third-party developers creating new themes and exciting add-ons for it, and the relatively high memory requirements ... but most of all the speed with which it functioned.
On the site you have under development at present, how much of the blame for how slowly it loads (and for me it loaded very slowly!) lies with that host, and how much of it lies with the PHPWebsite software, is hard for me to judge, as I have no experience with that host.
The site you are building is actually very well suited for either WordPress (using the "Pages" functionality) or Joomla! The present 5 "static pages" that comprise the site should place no load at all on the server (they are not really "static", because they are built from the CMS, but they are relatively light in functionality and have no memory or CPU intensive interactive features). To my thinking, a CMS is a bit of any overkill for that kind of site, but I still use CMS systems for such things as the site owner can make his own changes.
All things considered, from my knowledge of PHPWebsite, WordPress, Joomla! and other popular CMS systems that are readily available, I would use either WordPress or Joomla!, partly because they are so easily installed on DH via their "one-click" installer but mainly because of the huge selection of templates and add-ons, and their active user and developer communities.
Of those two, most feel that WordPress is easier to learn (it ought to take about an hour!), while Joomla! has more immediate potential for growth because of all the different modules available for it (much like PHPWebsite, but with orders of magnitude more tools available!). It is also likely to take you a bit longer to get your head around the way Joomla! handles "pages" and Sections, and categories, etc.
Bottom line, for that site I'd have to use WordPress if I wanted it up as quickly as possible. If I had some time to spend, I would probably do it in Joomla!, just to leave myself the flexibility and expansion capabilities available in case the site really took off and I wanted to add a lot of features later.
There are plenty of "features" also available for WordPress, but Joomla! is more of a "full-blown" CMS architecture than WordPress, which started out purely as "blogging" software and has grown to have more than enough CMS functionality for the kind of site you are presently building.
You could probably build a working and attractive WordPress site using the content already on your dev site in half-a-day - and that is including the time to install it and learn your way around.
I would just pick one of the available templates that was "close" to what I already designed (the DH installation comes with about 50, and there are well over a thousand available!), modify it by adding my already prepared graphics from the dev site, and copy/paste my content from the existing pages to the new ones.
Joomla! would also work very well, but you will need considerably more time to thoroughly explore and understand how it works than you will with WordPress - probably comparable to what you have invested in learning PHPWebsite.
All that said, do not let me discourage you from pursuing getting PHPWebsite running on DreamHost - it may well meet your needs and there is always a real value to "dancing with the devil you know!"