The age of the car puts this as having a 4 speed Rover box, not a Moss. The Rover 5 speed (LT-77) was introduced later in the year this car was produced. Moss boxes were only used up until around 1972 or '73...
You'll find an R380 very notchy and slow to change compared to the 4 speed Rover. Also the chassis (and body) is narrower than the later +8 which was fitted with the R380. I expect you would need major alterations to the transmission tunnel, chassis cross member etc. and that is assuming it will fit. I also expect the prop shaft will need shortening.
If you just want taller gearing, it might be worth investigating a change to differential internals to raise the gearing a bit...
Cheers,
