What was the solution in the end for you, please?The BB I have has twice as much thread as the one above. No reason that should be an issue but it's certainly a difference.
I guess I'm back in the market for a 73 X 113.
Webbline looks like a useful shop.https://www.webbline.co.uk/shop/bottom-bracket-taps-bsa-pair/https://www.merlincycles.com/cyclus-bsa-bottom-bracket-tap-230298.html
What is it about £50 for a set.
Up to you whether it's worth it.
May be cheaper to visit the lbs for this one.
Or simply use a different BB.