TBH I cannot see the proposals happening. Much of the land going to Lewes has been sold off and developed. The line towards Uckfield requires bridges and the landowners don't seem that keen for any railway to be re-instated.
If it was to go ahead and obtain the £millions it would require I suppose it would be a case of compulsory purchase from the society (and the private tenant still living at the station!) and re-location of the stock. Or more wildly, perhaps they could fund the trackwork and infrastructure and ask the society to run the services, similarly as the Romney, Hythe and Dymchurch railway runs schools trains.
I can' see it ever getting off the ground however, its just platitudes to the green lobby.....