Just in the interest of further transparency (there's a "Windows" joke waiting there, isn't there?) here's what the problem was.
With MySQL, you can have once instance of the database serving a number of people. They all have different usernames, and if you set up the permissions correctly, their databases are invisible to each other.
With PostgreSQL, it's much harder. Either people can see each other's databases -- at least the names, if not the contents -- or you lock down the schema information so much that a lot of standard and important tools just don't work. And because there are so many possible plugins, the attack surface for a hostile user is larger. So there's a risk of someone finding a way to read, or worse, modify, other people's data.
I think this is a result of the two databases' different histories; MySQL has long been used in multi-tenant environments where there are a large number of users who might be hostile. PostgreSQL has normally been used for smaller groups where there's at least an element of trust.
So, it looks like in order to support PostgreSQL properly, we need to have a separate instance for each person. This is doable, but a big change to what we intended to do originally. Sorry for the bad news :-(