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

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. 

I don't know how to answer this question.  Maybe start with measurements.  Frequency response, distortion, and channel separation?  I believe doing that leads nowhere. To start I compared my Cadenza Black to my ART20.  They are both balanced, neutral and all that good stuff, but they sound different.  I did it with a couple of others before giving up.  Forget it.  There is no right answer to this question.  At any given price point each of us must listen and choose, there is no other way.

Oh, I forgot to mention the element of subjectivity.  One man’s meat is another man’s poison.  My absolute favorite mono cartridge is the 2M Mono SE, which is the mono version of the 2M Black.  I prefer it to a $2,000 MC that shall go nameless so as to avoid offense.  I prefer my 2M Black to any other sub $1K stereo cartridge that I own, although I have one of the vaunted Shure V15 Mr w/Jico deals and a very good Stanton 881 that are also better to me than any of the MC in that price range.  But that is my preference and it goes without saying that YRMV.  Just additional grist for the mill.  This question is like searching for the Holy Grail.

We are such a nice group of guys. No matter how open-ended and vague is the question, some of us will earnestly try to answer it.