Further to the Honda auto engine oil consumption issue, this link clarifies what was happening. Seems the variable cylinder management system is the cause. Reading the article it appears that if the engine isn't under load, cylinders are deactivated resulting in no combustion. I'm assuming now, that with no combustion, the piston rings may not be expanding sufficiently enough to control oil. Interesting enough but certainly unrelated to what happening with the generator.
http://www.hondaproblems.com/trends/excessive-oil-consumption/
http://www.hondaproblems.com/trends/excessive-oil-consumption/