I think you'll get so many differing opinions on this subject, it confused more than anything else.
Think about this, the statements made in reference to the condensation in the exhaust system and what wasn't mentioned, the engine oil system by not having run an en engine long enough to expel all the water/condensation. This is a true fact and is very detrimental to your engines, gen set or main.
How do you keep this from happening? Either drive the coach, and I don't mean just down to the gas station and back.
It needs to be loaded to the point it achieves full temperature for at least one hour. This goes for any internal combustion engine.
Trying to make this short and to the point, and I hope I'm giving you the information you need to base your choice, to run or not to run the engines.
Ask yourself, will I have time to do it right? If not don't run it. If it's a gasoline engine, Stabil is your best friend, for the whole system. Diesel engines and fuel systems will tolerate long no run storage periods.
My choice, I do not run an engine on any (any) of my vehicles unless it's going for a ride. I've learned the hard way, for me this really works better than any of the exercising advice I ever gotten from anyone, including so called professional advice.
I hope that helps you in the long run. The battery choice, Keep them clean protected, and fully charged. As far as removal, that's also for the most part a personal choice, unless you live in a very hostel climate, or unable to properly care for them stored in the coach.
Dan & Loretta, US Army Retired Aero Scout Pilot
2012 Fleetwood Providence 42P Class A/DP
Spartan Chassis, 8.9L Cummins 450HP