In the end this will probably be just a pipe dream...
Once you bring in politics, I can see that things could happen quicker than you might expect.
Ken gets in, and very quickly TfL is ordered to take over the lines ASAP. And if, given the last time, they take over any other lines - the chances are the actual changeover/upgrade will take place over time. So, they will put in the 'temporary signs', throw 'London Overground' vinyls on whatever base colour the trains have and so on.
But, what might happen sooner (which would be a good thing) is they'll ensure stations are staffed for longer, if not all the times trains are running.
I guess it all depends on what happens next year. It certainly makes sense that another option could be to simply incorporate part of an existing service into the LO brand - but keep it under the control of the current franchise holder until renewal.