Koetsu compliance compatibility issues

No one is likely to have the breadth of experience described by Syntax. However, my Koetsu Urushi, which seems to be at least a bit higher in compliance than your Black, ran well in my Triplanar (effective mass = 11 gm) but is even better in the Kenwood L07D tonearm, with the stock 12-gm headshell. I could believe it would benefit from a higher effective mass tonearm like the FRs.

Geoch, You wrote, "So, don't bother. You simply can't trick the formula."
But in fact the formula itself is "tricky" and only gives you a ballpark estimate of the resonant frequency, even if your input data are accurate with respect to one's particular sample of a particular cartridge. So my approach would be to forget the formula but to try in a general way to match a low compliance cartridge with a medium to high mass tonearm, etc, etc.

I am one who does use ESLs and OTLs and who does very much like the Urushi that I own. I also have a Colibri and an Ortofon MC7500 and several tonearms and turntables. Many days, I prefer the Urushi over all. I don't think a 12" arm is necessary to enjoy the Urushi, but when I finally acquire one, I will try it.