Sully, there's lots and lots-o posts on Cub Cadet Drive System Fluid Plus and it's alternatives. Most associated with 2K series machines, but the transaxle in your more rare 3K, is the same, but slightly larger capacity with auxiliary outputs for P-steering, etc. When I researched it some years back and had conversations with Hyrdo-Gear (maker of the hydrostatic drive on these), the Cub oil was made/supplied by Shell. The Shell name for it is Shell TTF-SB. The spec sheet for it closely resembles normal, run of the mill engine oil. The Hydro-Gear guy agreed that they typically spec 15w40 HD engine oil for their drive systems, but their customers customers can surely spec their own, provided it meets HGs requirements. I run commonly available Shell Rotella-T 15w40 in my 2544, and would probably run Shell Rotella-T 5w40 if I used it in the winter. I personally would not hesitate to run this in your 3K series. I don't know of a any modern day, LT/GT hydrostatic, shared drive system that doesn't use motor oil.
Joel