I don't think a new Bourne End direct chord is feasible. It would have to be built right on top of Donkey Lane so you'd probably have to buy up every one of the estate properties on that road as you'd be removing their access. Six houses at say £2m a pop, that's £12m before you start digging. Granted you could redevelop and recoup some of that, but imagine the politics and ill will trying to CP these 'beautiful waterside family homes' etc. Besides the curve radius would be around 120m, probably unacceptable today without special stock and noisy for any remaining local residents. Certainly impossible to build a compliant heavy rail platform alongside such a sharp curve with acceptable stepping distance.
Better to replace the current junction crossover with a new slightly shorter fully signalled scissors arrangement slightly to the west of the existing junction. Platform starting signals could be placed almost on top of the switch tips as at some London termini, and co-acting duplicate signal heads placed low down on the posts pointing towards the cab window to make best use of the platform length. I think a 3x20m car train might be squeezed into both platforms with these measures, together with some judicious adjustment of the buffer stop positions. A 4x20m car train might be accommodated in platform 2 with the London end car hanging off the platform foul of the crossover, and with the off-platform vehicles's doors isolated by SDO. An additional outer starting signal beyond the scissors could control departure of such a train. A diagram is in preparation . . .