We just need someone to develop an air-to-air battery replenishment system (same theory/model that you see in use with military tanker aircraft for air-to-air refueling).

I can see it now. Max weight/batteries on take off. Controller to drain batteries serially, and as each one is exhausted, chuck it out the bottom of the plane (with some kind of landing/recovery mechanism). When you start running low on batteries, re-fuel at the nearest tanker.

Obviously I'm kidding. The tanker model is ridiculously expensive. That's why you only see it used for extremely critical things (military).