I have a History of Art database with 30 tables and complex relationships between people (the sitters, artists, etc) and the works (paintings, sculpture, etc). Currently this is implemented in MS Access with about 5k lines of VBA code and 30 odd forms. I have to make the choice to either use a PHP framework or to use a CMS. I have PHP coding skills but not much time, so can't really afford to spend a long time evaluating the CMS products to see whether they can be adapted to use a different data model.
My question is whether the popular open source CMS products such as Joomla or Drupal allow use of a custom data model, or do they expect you to use their built-in model (articles, blogs, comments, etc.)?
Using a CMS would be inappropriate - whilst many of them do support custom properties they don't usually implement them as fields in a relational database (thus making it hard, if not possible, to sort or index by).
I suggest you recreate your MS Access database in MySQL and then use a Scaffolding framework (Ruby-on-Rails has a very celebrated scaffold) to automatically generate code and GUI for you, then you just tinker it as needed.