I am looking for an open source project whose goal is to create a
webmail interface with an architecture similar to GMail's; that is,
the client is implemented in JavaScript that generates a DOM tree
based on raw mail data downloaded from the server.  The advantage of
this approach is that it allows better interactivity for the user.  It
has surprised me that I can't seem to find any open source
implementation of such a system, so I am wondering if maybe I just
don't know where to look.  All of the existing Open Source webmail
solutions I've found are very traditional client/server web apps, with
all the work done on the server and lots of roundtrips.

Just a comment -- my experience with OpenWebMail and SquirrelMail has
been very similar to yours. DHTML is definitely the way to go,
although GMail needs to start supporting all of the major browsers
that offer the necessary capabilities, in my humble opinion.