Hmmmm. I don't think all of it is correct.
AIUI, the LMS was impressed with the Castle and did want to buy a batch from the GWR (50 sounds about right), but they were stopped by the government (would that have been the Board of Trade?) because it was deemed unfair to the private manufacturers. (I'm not sure why, possibly because of fears of cross or hidden subsidies.)
I'm neutral on the 'lending drawings' question, ie I don't know.
However, on the story of the SR lending drawings to North British, I believe evidence shows this is a myth - poppycock, even.
About 15-20 years ago, on the then LMS e-group, this story was discussed. In the group was an older gent who had worked as an apprentice in the North British drawing office. He was there when closure came, and knowing history was being lost, or threatened with such, he went through the drawing office files, and found hundreds of blueprints, all carefully numbered and recorded. I think he actually mentioned some interesting classes/designs, which I've forgotten.
But of Lord Nelsons there was no drawings, nor trace of such, ie no missing numbers around the time that any drawings that might have come, been recorded, but subsequently been lost.
He concluded there were none, and never had been. My thesis is that in the mid-1920s, it would have been normal around the bar room table (or platform trolley if under 18) for folks to talk about the similarity, at least externally, of the LN and parallel-boilered Scots, and this is how the tale began.
OF course, they looked quite similar, they were both designed to do similar jobs within the same loading gauge - but equally, in the guts, they were about as different as you could get - the LN was four-cylinder, the Scot was three, although they both had Walschaerts gear, of course. But if the whole point (as the myth goes) was for the LMW to 'big-up' its locomotive fleet ASAP, why go to the bother of redesigning the cylinder arrangement, and all the valve gear and associate gubbins?
My conclusion is on the lines of the NB draughtsman, largely based on his research. It is simply false.
Now that sounds a highly cost-efficient solution: no more outlays on separate designs, more parts, just knock up another what, 15 x 47xx?
What improvements were needed? I thought the 47xx were supposedly good machines, bar their RA?