DrJava should provide a dialog (similar to "Go To
Line", Ctrl-G) called "Go To File" (Ctrl-Shift-G). It
contains a text box that allows you to enter a file
name. When you press OK, it changes the current
document to the file entered.
As you type, the dialog auto-completes the file name
(based on a list of files in the project/flat file
list) and makes suggestions.
Basing this on file names as opposed to class names
should make this possible without light-weight parsing,
and it should still provide a lot of value.