Why don't you fog the genny, drain the carb and you won't have to exercise it at all. I have been doing this since I got the genny. About 4 years now. Get the spray fog, remove the air filter, start the genny and then spray the fog into the air intake until the engine stalls out. Then drain the carb. I take the battery out along with the 2 house batteries and put them on smart chargers. The genny is a 4000 watt Onan which is called a juice box. It goes into the trailer hitch at the back of the 5er.
Here's a site for this one. Not the one I use but it's an example. AMSOIL Engine Fogging Oil