I can see both sides:
I am thinking the F525 is 12-15 years old, maybe more.
The original specification was for 10w30 when it was new. The multi-viscosity oil was probably to keep the transaxle happy when it was cold. Hydros like thin oil during their warm up period.
Now, most of them have probably 600+ hours. With some anticipated wear, probably when warm at least, the hydro will perform better with 30 wt. oil in it.
And also, the current Kawasaki engine specs call for 30wt. oil if the engine is operated at over 80 degrees Farenheit ambient temperature. Because they don't burn quite as much 30wt. oil as they would 10w30. All these engines burn some oil. The older, the more oil, although I am told that an ounce per cylinder per hour for a new engine is not unreasonable. So check the oil level regularly.
Its really your call which weight oil to use. I would recommend you use Kohler, Kawasaki, or Briggs and Stratton brand oil, as these oils still have zinc in them and I am thinking the zinc helps the oil to cling to surfaces inside the engine when it is stored.