I have a neighbor with one of these that I service. I use the Valvoline Advanced Synthetic 20w50 in both the engine and the Hydro drives, and a Fram PH4967 for the engine oil filter.
I believe Kawasaki recommends and sells a 10w-40. That being said, there is Rotella T6 15w-40 and Mobil1 15w-50 readily available. I would use one of those readily available oils over some overpriced boutique oil. Just my two cents.
Either oil you are leaning towards will be fine. The important thing for you to do is blow your machine off after each use. Another important thing is to check the oil each time before you use your Mower.
I believe Kawasaki recommends and sells a 10w-40. That being said, there is Rotella T6 15w-40 and Mobil1 15w-50 readily available. I would use one of those readily available oils over some overpriced boutique oil. Just my two cents.