350 hours over ten years isn’t what I would call a lot of hours.
Now to the oil. Kawasaki recommends 10W40 under normal conditions. 20W50 is acceptable in high temperatures or if it’s using oil. Kawasaki 10w40 is fine. 10w40 4T motorcycle oil will work. 20w50 v-twin motorcycle oil will work. Valvoline VR-1 20w50 will work. Mobil 1 15w50 will work.
15w40 HDEO (Diesel oil) will work. I’m currently using Rotella T5 15w40 in my Kohler. The oils that I listed are high in zinc and phosphorus content, over 1100 ppm of both additives.
Now to the air filter.
@bertsmobile1 has given good advice on the air filter. I would like to add to his advice. If you are not currently using a foam pre-filter over the standard filter, you should get one. Remove the foam pre-filter every 25 hours, wash in hot soapy water, let dry, and apply a light coat of foam filter oil, before reinstalling. Most motorcycle shops carry foam filter oil in spray cans.
It’s 100F today in my part of Georgia so, I know about the summer heat you are experiencing.