I think this is a misunderstanding. First, electrickery will only be produced when heat is wanted, it will not run when heat is not needed. Now the 'inefficiency' of the generating system is guess what - heat! And this heat is harvested in the usual way to run your heating and HW. In other words nothing is wasted, so there is no real inefficiency in leccy generation.
The 1/3 price electricity is just a side benefit. You will only benefit from it when net metering is available: when it isnt it would be prohibitively complex to make use of the benefits. And when it is, you dont get anything like as much as you pay for your leccy, the rate is way lower. The end result is that although microCHP is great in principle, it isnt great in practice today for home use.
Now if you had a few houses running on a private generator, installing CHP would bring you big benefit. But its 99.9% likely that youre not.
Whats the way forward with microCHP? One possible way would be a unit that produced your whole leccy requirement, 10kW rather than 1kW, and with say 33% efficiency. Then you could run with no leccy grid connection. In summer your leccy would cost the same, and in winter it would only cost you gas price.
If you were willing to install a load shedder you could safely cut that back to 4kW.
Regards, NT