Whilst the obvious option with both the Uckfield line and North Downs, Marshlink routes is to extend the 3rd rail, as has been discussed many times within these forums, there are other possibilities.
I don't see why longer trains will particularly be an issue for batteries as each unit would have batteries for itself. Schemes have so far focused on areas where you can recover a failed unit quickly, because it's still very much in the operational proving stage.
Whether the trains are 3, 6, 9 or 12 car trains they should have batteries every third car either under the passenger area or as in class 755/756 units within a smaller power carriage.
On a personal level I would also add into the trains ways that power could be regenerated back into the batteries while travelling with regenerative braking and having solar panels on the rooms on either all carriages or every second or third carriage that could recharge the battery on route even if the train is operating on 3rd tracks or OLE. But as a backup I would have Uckfield setup with OLE setup at the station so if needed, trains could recharge the batteries. The setup of OLE power point should also be setup at Rehill, the problem there though is that you would also have to do the same at Gatwick possibly for the trains that start there. For Marshlink the OLE power points would be Ashford International and if the service is extended back to Brighton, then the one of the same platforms used for the Seaford/Eastbourne - Brighton platforms should be if possible converted to have OLE Power point as well.
Now, I know there may some people that will say that you would only be able to get energy from a solar panel when it is sunny, but that is incorrect with most modern solar panels you can actually get energy whether the day is cloudy with rain or being a 30 centigrade sunny day.
When it comes to the OLE power points those can be setup with little or no interference with the 3rd rail pickup supply as is done in a good few places within Network Rail whether within the Southern or Merseyside areas.
The problem with extending the Uckfield and Marshlink routes to have 3rd rail, is what the lifespan of 3rd rail. Will 3rd rail still be around in 100 - 150 years time? Or do we just think of what is needed today, to help the environment and take away the need to be using diesel trains on the Uckfield and Marshlink routes?
Whilst the above are just ideas, the answer really comes down to what budget will be available for any for changes to be made to systems and as asked above, what is the lifespan of those ideas?