MGB pats will not fit as the engines are totally different. However, there was another conversion done with a B series engine and box from an 1800 "Land Crab", and on those MGB tuning parts do work. I have seen one at an exhibition in Glasgow over 40 years ago. The company concerned was also selling a Ford crossflow to A series (or was it 1800?) transmission conversion, which of course had fair potential.
Someone else at the same exhibition had a Rover V8 on a Landcrab transmission, and suggested that it might be squeezed into a Mini. I doubt it, but at least the weight might be tolerable, the ali V8 being light for its size. It would probably go, with extreme difficulty, in an 1100/1300 which are much wider and have a longer nose.
I definitely am in favour of this Mini being fitted with a proper steel front. Much safer.
There are subsequent BL engines that were derived from the Maxi E series engine. The R series, 1600cc only, was used in the Maestro and was not very reliable. Then came the greatly improved S series, however both R and S used an end-on transmission rather than in the sump, and as such are probably too wide for a Mini.
Then of course came the excellent, if properly maintained, K series, and there is plenty of proof on this forum that they can be fitted to a Mini, with some difficulty. It might be better to rebuild this one with a K series, which would solve the weight problem.