Complete crayonist idea, how about simply putting wires up on the line & extend some of the stations, to allow 80 metre stock to call (ie a single 350)
The stations with little demand (like Fenny Stratford & Kempton Hardwick) could be closed.
Removes a diesel island (not sure how much wiring there is at the Bedford end but I'm sure the wires extend at the Bletchley end due to the depot. It's the sort of line which could be run with buses for X months to do the work in one go.
Also has a benefit of allowing the EMR 360s to reach Northampton under their own power to avoid needing to be hauled via London behind a diesel loco.
It's not completely mad - At Bedford the bay is wired and the goods loop is wired almost to St Johns for TL shunting, so there are supports in place to hang the registration arms over the U&D Bletchley, so the junction tie-ins wouldn't be too bad. The bay is 80m long, so may need work to accept a 350. Bletchley end, the connection up the branch to the sidings is wired, so again a relatively straightforward tie-in there. Platform 6 is 120m long, so no problems there. Power wise would presumably be easy as well, given the minimal demand.
There are some problems - 350 SDO is only available on a whole-unit basis, so you'd need to extend every platform to take a 350. I count 12 overbridges of various types and ages that would need to be assessed for rebuild - About half look either clear or relatively simply to sort out. However the big problem would be the number of level crossings, I count 12. Any changes required to make them safe with wires could well blow the budget.
So it's not totally out there, like building a new line from Wolverton via Olney to Bedford, but it isn't going to be a quick win, and it's going to cost a lot to address the lack of investment in previous years. I suspect electrification will need to wait for EWR to come along, either as part of the project or following after it's done the enabling works like Signalling, Platforms, etc.