At 300-400 hours a season, I think changing the oil every week is way over the top especially on engines with oil filters. Running them for hours at operating temp is the ideal condition for the oil, since it burns off all the moisture and fuel.
Kohler's recommendation is 50-100 hour OCI's depending on which engine you have (oil filter vs. no oil filter). Even if you did 50 hour intervals that isn't a change every week. Using synthetic and changing it that often is a huge waste of money. They would be fine on any HDEO like Rotella 15w40, SuperTech 15w40, Rotella 10w30, etc.
While small engines do run a bit hotter, they aren't necessarily hard on oil. As long as it is kept full you will be fine. I have a customer with Scag and Bobcat mowers who changes the oil once or twice a season with the cheap stuff, not even a HDEO, and his mowers run great. If you change the oil say once a month, that is still fairly often and you will be saving a bunch of money to put toward your business.