Upgrading from NAD 320 BEE?

At your price, I repeat myself: get the Moon LP3.

I have to say that I love that so many of us have such great memories and/or experiences with NAD gear. I ran a pre (104?) and power (204?) amp combo as my first 'hifi' gear starting 16 or so years ago. Great, great equipment that is just plain hard to beat without spending significantly more.

The only other candidate that I might throw in that I think is of the same ilk is the Creek 5350SE. They seem to go in your range with a very solid MM phono stage.

If you go down the upgraded phono amp route, then on the lower end of your range you must think about the Bellari VP130 if you intend to use MM cartridges. This units sounds really nice.

The upper end of your range is crowded with good deals like these:

Lehman Black Cube Statement
Grado PH-1
Musical Fidelity X-LPS v8

or, if you can spring for a little more, look at the Musical Surroundings Phenomena II - or try to find an original Phenomena used.

Good luck.