The more I think about turning the D78's into diesel trains, the more I think that they should be converted into DEMU trains with the ability to travel with diesel or OHLE as I believe that they are the same height and size as Class 313s?
They are being turned into DEMUs, as they will still be using electric power bogies, not mechanical (as on 1xx DMUs, or DMMUs (DmechanicalMUs)). DEMU doesn't imply anything about being able to run off an external electric supply, only that it's electrical transmission between diesel engine and traction.
Adding alternative OHLE power source to them would be quite possible, at a very large cost, but probably unlikely to be worth it. The 60mph limit on them means that they need to stay away from the major electrified main lines. OHLE isn't necessarily any more green than diesel anyway, as the nationwide electrical supply now has to be supplemented by big diesels (think Valenta-sized, lots of 1-2MW units spun up as required) for peak capacity, due to a lack of capacity in the big generating stations.