Pure speculation on my part but, as the platform in question is on the down side, I think the GC would have used their own line up to Helmdon and linked up to the N&BJR line there.
If they were going to build a new 'direct' line the convention would have been to have the platform on the up side.
I should think the N&BJR directors and shareholders would have been fairly amiable to the idea, glad to be rid of a ramshackle concern, but I bet there was a lot of opposition from the LNWR and, presumably, as they would require running powers over their metals into Northampton, it was never taken any further. Certainly no bill was ever presented to parliament.
As I say, these are just my rambling thoughts, the branch is an interesting idea though.
I take your point about the different elevations, about 60ft if my memory is correct. That would need over a mile of 1 in 100 so, as you say, it would be impossible within Helmdon, but perhaps to the south of the village over a longer distance.
Sadly we will never know their thoughts, but in those days they often built thinking of the future (most of the SMJ was engineered for double track) so perhaps we are reading too much into that platform.
Still, an interesting 'what if', even if Dr Beeching would have closed it!
During the construction of the Great Central a very steeply graded temporary link was laid from the E&WJR to the site of Helmdon (GCR) station purely for bringing in heavy materials for construction of the GCR.
I can't find any suggestion of a GCR line to Northampton in such works as George Dow's monumental 3 volume 'Great Central', but I believe the Northampton and Banbury did consider a direct route from near Blisworth over the West Coast actually to reach Northampton.
The GCR did seem interested in the E &WJR at one time, with several prominent Great Central investors acquiring East & West shares. C W Bartholomew, son of a GC director, held enough E&WJR shares to be allowed unofficially to frequently drive trains on the line and also to take his miniature railway under the E&WJR's bridge alongside their main line track at Blakesley! It was all leading to a possible GCR route to Birmingham via a doubled track E&WJR and Stratford Old Town, either from Woodford West or from near Morton Pinkney, but which the GCR soon abandoned when they joined forces with the GWR to build the joint line through Wycombe in order to avoid relying on the Metropolitan Railway as their sole access to the London area.
Another link between the SMJR and GCR was Mr Wilmott who prior to taking over directorship of the E&WJR ( soon to be SMJR) had been Sheffield area manager of the GCR, his son also became a GCR area manager.
It would appear indeed that they had a potential vested interest Dick.
A quick look on the map I would think the line would have run from near Radstone to between Wappenham and Helmdon. I wonder if there would have been some rebuilding of stations?
On a group on Facebook regarding the GCR and the remains, the fact that the platform is effectively on the wrong side of the line was raised. I believe that trains from Northampton would use the main platform then once empty re-position and wait at this platform thus leaving the mainlines clear.
According to the same source, no act was ever presented so the line was only ever a dream that was never documented.
Brackley Central Station (built 1897 by the Rugby firm J. PARNELL & SON) was unique on the line. The MSLR had hoped to use the (A43) bridge for public access to the platform, but local opposition meant that the booking office had to be built on the embankment overlooking the line. The platform was reached by a footbridge spanning the down line, instead of a staircase from the centre of the station bridge (no.525).
The MSLR planned to build a locomotive shed and workshop at Brackley, but was opposed by the Squire of Turweston, John Locke Stratton, Mayor and major landowner in the area. The MSL decided to construct their engine depot at Woodford, some 10 miles north.
Opposite the down side platform, on an official plan of Brackley Central Station, the words
should be noted.
The Metropolitan Railway, extension to Moreton Pinkney. Charles Liddell, engineer. Deposited 30th November 1889.
Railway no.1. From a junction with the East & West Junction Railway in Canons Ashby; through Moreton Pinkney, Sulgrave, Helmdon, Wappenham, Radstone, Brackley, Westbury and on to Quainton.
Railway no.3. From a junction with the East & West Junction Railway, terminating in a junction with Railway no.1, all in Moreton Pinkney.
Railway no 4 & 5. From a junction with the Northampton & Banbury Junction Railway near Helmdon Station, to a junction with Railway no.1, all in Helmdon.
Note that in the last statement the junction near Helmdon Station was to be ALL in Helmdon, perhaps you were on the right 'track' after all.