If you leave electrifying the difficult bits until the rest is upgraded and running more and longer trains then you increase the cost and disruption of the closures you will need and just make it even less likely to ever happen.
So don't waste any more time trying to develop and commission any more hybrid trains, just electrify it all straight away then, especially as there
isn't even a difficult bit, apart from some houses close to the track at one point.
In terms of closure time, I think it still might be worth considering temporarily reinstating one of the other tunnels to enable a through service when the main tunnel is closed.
So long as the tunnel is structurally sound, the temporary track could be low speed and reversible, and built with components that could be reused afterwards.
There's nothing temporary about it! All the tunnels are sound, and the two single bores could easily be brought back fully into use and electrified to allow the double track bore to be done. The single bores have been maintained because they are listed as strategic assets that cannot be allowed to deteriorate. It is likely that all 4 would be needed anyway (as the western end of the 4-track railway from Yorkshire.)
The canal lobby (including a certain Welshman) will scream about this, but I think it could easily be done if the rails in the single bore nearest the canal were paved to allow the C&RT to escort boats through for a couple of windows mid-morning and mid-afternoon while trains were restricted to the third track (signalled bi-directionally, if needed.)
As has been said in another thread, why complicate the modernisation of a trunk route with gimmicks to get round a what is really just a basic failure to invest in infrastructure outside (or not serving) London?
I have suggested before that
if restricted clearance is making electrification difficult in places across the network (big
if) then low wires and a speed-restricted narrow pantograph could do the job in most of these places. If BR could build narrow trains for some lines, how come we can't cope with a narrow pan for some short sections? (The Forth Bridge was the earlier example.)