Remembering that whatever goes up must come down, although the power drain is larger on a hilly line the opportunities for energy recovery are also similarly larger. Obviously the laws of themodynamics mean you'll still have a greater net expenditure of power if you are applying and recovering than coasting (impossible to achieve 100% efficient transfer of energy type), but the difference isn't as large as is maybe being suggested.
Fitting a 100-mile range battery to a 4-car EMU should not be particularly impossible, especially if it's a currently manufactured design. That would comfortably cover Hurst Green to Uckfield and back with room to spare. There are various options for emergency-only shore supplies at station. Additionally, a short extension of the third rail, 'around the corner' as it were, to allow trains to accelerate away from the junction or hold at a red on the juice rail would be a perfectly sensible provision.