I'm late to the thread here, for which I apologize.
I have used both kiryu and european pumice for some time now, mixed with akadama and whatever else I have handy. I can tell you that kiryu and pumice are very similar in texture, weight, water retention and drainage properties. ç
But Kiryu has one advantage, it changes colour drastically when wet, from off-white to orange-brown. This makes it an excellent top dressing. Last year I was using pure kiryu as top dressing, and it dries too quickly in the harsh spanish sun - same as pumice. This year I think I now have the ideal top dressing, kiryu and akadama 50/50 mix, small granules, about 2-3mm (1/10"). The akadama component retains water longer, and changes colour when wet, so is also good as top dressing. Except the small particles of akadama start to break down on the surface after 9 months of watering. The kiryu holds structure, so the 50/50 mix is great.
And for completeness: in the main soil I use larger kiryu/pumice/akadama particles - around 4-5mm (1/6 - 1/5") . As kiryu is about double the price of pumice, I buy pumice for this. + some lava for extra weight in shallow pots or pine bark for extra retention in deeper pots.