Adding electric traction to an existing type of DMU does indeed sound very complex, and possibly not worth the added costs and complexities.
A somewhat similar result could be achieved by a new build of high powered EMUs with at least twice the usual HP per ton, these being compatible with 159s
A train could then leave Waterloo with the high powered EMU hauling or propelling the dead DMU, as far as Basingstoke. At Basingstoke the electric unit would be detached, and the 159s run onwards under diesel power as they do now.
This would increase capacity on the inner part of the route, and eliminate regular diesel running in or near London.
The special EMU could be based on standard technology, but with every axle of every vehicle being powered.
A bit like an updated version of the old REP units.
Another option would be to re -form the 159s into 4 car sets by the addition of an extra and high powered electric motored vehicle. This would be simpler operationally, but would reduce performance under diesel power.
The problem is that most splits of trains happen at Salisbury, meaning that you'd have a massive loss of capacity between there and Basingstoke.
You'd probably be better off electrifying to Yeovil and running :
- 1 tph Waterloo to Yeovil EMU
- 0.5 tph Waterloo to Yeovil EMU with connection to DMU service to Exeter (cross platform change)
- 0.5 tph Waterloo to Exeter DMU
With the EMU to DMU connection, as the EMU would be faster the extra time required for the change can be gained back over the EMU section.
You could increase frequencies between Basingstoke and Salisbury by extending the Basingstoke stoppers. As although few would use them to get to Waterloo, it could provide a much better local service (as well as freeing up platform capacity at Basingstoke and possibly allowing for the opening of a station near to Oakley where there's a LOT of housing being built over the next 10+ years).
It should be an easy line to wire up; as it's got fairly modern signals, has few junctions and a lot of the bridge works (should easily allow electrification, but was probably to the old standards) have been modified/sorted for freight.