Now that I have my Tri-planar tone arm, I ask for recommendations for a new cartridge.

Those Miyajima cartridges are very fine indeed, but aren't they low compliance?  In my experience, the Triplanar does its best with "medium" compliance cartridges.  For one example, the Triplanar never got the best out of my Koetsu Urushi, whereas it does very well with some MMs and the AT ART7.

Mu-Tech Hiyabusa. I use this on my Tri-planar Merrill-Williams setup.

1+ Lewm

Atmasphere has a Tri Planar. You might ask what he uses.

The Japanese comment is way off. You are forgetting about Grado, Clearaudio, Soundsmith, Ortofon, Van den Hul, Goldring and others. The Japanese have not developed anything. Joe Grado invented the MC cartridge.

 Clearaudio and some Ortofon cartridges as well as all Lyra cartridges are a great match for the Tri Planar as are Dynavector cartridges. The Ortofon Windfeld Ti is the real overachiever in your price range. Any medium compliance Soundsmith would be great. You can use a low compliance cartridge. You will just have to add some mass. Lighter systems have less distortion than heavy ones. 

Miyajima Madake 
review: 

http://highfidelity.pl/@main-562&lang=en

The Madake has an old school cantilever with a pressed in stylus leaving unnecessary mass at the most inappropriate place, the very end of the cantilever. In comparison to a Soundsmith ruby cantilever that thing is a baseball bat. I don't care what it sounds like. It can not possibly track as well as a more modern design. For me it is a total non starter. I am also not a huge Shabata fan. I think the GygerS, Replicant 100 and Soundsmith OCL styli track more quietly. Not sure why, but that is my experience. AT's ML stylus is also excellent.