turn on the "close editors automatically" option (preferences > General > editors), which will close editors automatically when the limit is reached an a new editor is to be opened.
make use of multiple windows each with a set of editors for areas you are editing or browsing or searching
I've discovered that while it is true that you cannot have multiple rows of tabs for the same code-space, it is possible to have multiple rows of tabs showing on your window at the same time:
To accomplish this, simply drag a tab up to your title bar and release. It will create another row of tabs.