How can I get iTunes not to consider "Various Artists" an artist in the artist view?
I only really see two options here.

1) Get rid of the Album Artists field altogether, select all tracks and Get Info. Set the Album Artist field to blank, meaning song are grouped solely by their Artist and not Album Artists. The songs in the various artists albums will still be linked by the album name if you just want that album.

2) Create a smart playlist with the filter being Artist is (or contains) "The Monkees". This will, of course, filter all Monkees songs into the playlist regardless of the Album Artist.

Beyond this, there doesn't seem to be much room for configuring various artist albums better.