Best choice for approx. $3000 cartridge on VPI JMW 10, TNT III

I can get a new (NOS) ZYX Airy 4D, Koetsu Urushi Gold, or Koetsu Urshi Vermillion.

I currently use a ZYX Airy 3 and love it - Warm , 3D, detailed, natural sound.

Are these a big step up in sound??

What is your experience? Please describe any improved sonics.

Are these cartridges too "old in the tooth" compared to the current choices?

System........  JMW 10, TNT III maxed out, Pass Labs amplification, Magnepan 3.6

With that budget, you can buy a nice mc cartridge for sure. Personally i’d recommend the Miyajima Shilabe cart at or near that price point. I’ve heard that cart on a Transrotor Fab Bob tt with an SME tonearm & it has lovely rich tone, resolution & has a body made from rare and beautiful African blackwood. It is a widely reviewed cart for good reason. I couldn’t advise you how it compares to the other carts you mentioned as i'm more of a digital guy, though I’d suggest reading the reviews which will give you a good sense of how it performs. Cheers.
I’d buy a Dynavector Te Kaitora. 

I’ve owned all the Dynavectors and in a good tonearm the Te’s performance is close to the XV1-s. 
I have not had a chance to try any of the ZYX carts, but have tried a few Urushi variants.  I have a TNT II with a Graham 1.5 and now use a Kiseki Purpleheart.  They can be had for $3200 and is a fantastic cart.  From the Kiseki website:

VPI Founder Harry Weisfeld seeks cost-no-object performance for his own listening.

"I use the KISEKI Purple Heart N.S. in my own personal system on my Avenger Reference and have no urge to change cartridges. It sweeps you out of your seat and into the concert hall with power, grace, and air. I cannot recommend a cartridge higher than to say I use it when I just want to enjoy music."

Another vote for the Kiseki Purple Heart and good enough to be the second cart on Albert Porters table!