By my reckoning the 379 manages half as long on battery only as it does charging & running on the electric power supply. So, using your figure, 94 minutes on the juice would give 47 minutes on battery. But you reckon 68 (2*34) minutes is needed on battery so it is not going to work by 21 minutes. That is roughly eleven minutes each way if everything else works fine (no delays and good batteries).
Along the lines of the Paisley Canal suggestion perhaps enough electrification can be done cheaply to get rid of that eleven minute gap. Actually if eight minutes of route were electrified there would be a gain of four minutes on battery life/range. So eight minutes of route electrification gets rid of twelve minutes battery use each way. So Network Rail could electrify the easy bits and/or power hungry bits (up a gradient or group of stations where all services stop).
I can see that the best use of a Battery EMU would be on routes not completely electrified but where the gaps are sporadic so not the whole of one end of the route. That could be the North Downs Line. However what we normally need is something that can run on the outer reaches of a network beyond the currently electrified conurbation.
For the third rail electrified part of Southern I can only think of five cases.
Basingstoke to/from Exeter - hopelessly far off the juice.
Basingstoke to Southampton via Salisbury - not sure what percentage of this is gaps, most of it ?.
Oxted to Uckfield - probably too far but doable with some infill (charging at the Uckfield terminus).
Hastings to Ashford - probably OK as its part of a through service from Brighton, both ends are already electrified.
North Downs line - as above it seems the most doable as the gaps are spread out if some more electrification is done.
The above indicates a not very large requirement so would a manufacturer be interested. Possibly yes as a prototype derived from a production train (class 379) already exists. I wonder if Vivarails D78 conversion would be useful for any of these with a third rail capability left in. Plenty of power hopefully (for the chalky mountains) but a restrictive top speed for most of the five cases.
Of course the 442s have a better top speed

. Maybe convert all of them to Bi-Modes

. Pity about the door spacing

. All credit to Minstral25 for triggering that idea.