What are the most balanced relatively neutral cartridges at each price level ?

Agree with @jperry - Ortofon, other than the SPUs

Huge fan of the PM series by Nagaoka. 

level 1 - up to$1k. Ortofon MC Quintet Black

level 2 - up to $3. Ortofon MC Cadenza Black

level 3 - up to $5k. Ortofon MC 90x or for a few dollars more MC Windfeld Ti

level 4. - any price. Ortofon MC Diamond

At best, you will get different responder's preference at each price level, and not necessarily a preference based on your undefined terms.  I will contribute some of my favorites at or near level 4:

Audio Technica AT ART1000 (recently discontinued at $4950)

Audio Technica AT ART1000X (new model I have not yet heard at $5,500)

I think it is a great question. I think folks that are very experience with different cartridges and systems can generalize about the sound of cartridges. Folks with little experience would not be very good judges. 

I for instance use a Koetsu Rosewood Signature. I would not consider it a neutral sounding cartridge, it is very warm and musical. I own it, and love it, but would not offer as a contender. 

I think if we had lots of folks with extensive experience offer their opinions we would get a convergence around a couple different lines.