How can I fit a bigger rear tyre when limited by the front derailleur?
Put a larger tire on the front and don't worry about running a larger tire on the rear. 

Back when North Shore BC riding was just starting to take off (i.e., 1990s) we often did this setup as we were equipment limited. At the time the "thinking" was that it was bizarre ride a tire bigger than a 2.0 anything but a dedicated race downhill bike. So we would often swap a fork and run bigger rubber up front as there was clearance issues in the rear. Now  25 years later and anything less than 2.3 is pretty much considered anemic for most riding. 

Anyway, the mismatch tire size works fine. The front is where you are often traction limited as you brake and steer with this tire.  A small rear tire may mean a bit harsher ride (i.e., higher pressure with all other things equal) and a tad less traction, but you can afford this compromise on the rear.

Plus, one tire is cheaper than two, and if any one asks just tell them the setup is more aero (#AeroIsEverything - /sarcasm).