There are a number issues to consider before embarking on a change of gearbox.
1) Originality and whether this is important to you now or potentially in the future especially if your Plus 8 is one of the 19 Lightweights.
2) your wheel size and whether you are running on 5.5J 15" wheels or the 14" Millrace wheels that were introduced for the 1975/76 Lightweights and 1977 onwards 5 speed Plus 8s; the LT77 allowed smaller wheels and lower profile tyres whilst allowing the tyre rolling radius and therefore overall gearing to remain more or less the same as the earlier 4 speed cars.
3) the distance from the bellhousing to the gear lever position; note that the Mazda gearbox conversion is aimed at MG Bs and both 4 and 8 cylinder cars used the same all-syncho 4 speed gearbox (Dave W, can you confirm?) and this is not the same gearbox as the Rover V8 4 speed gearbox.
4) clearance to the handbrake lever may be compomised as the lefthand side of the Mazda gearbox is bulky and may cause fitting problems.
5) potential mounting issues although your car will have a variant of the 5 speed chassis and this together with the centrally mounted clutch slave cylinder should mean that this part of the changeover may be relatively straightforward.
6) a new gearbox mounting will have to be welded in.
modifying the handbrake lever mounting (necessary for the LT77/R380 and almost definitely required for the Mazda 'box.
7) modifying or re-making the gearbox tunnel cover together with associated re-trimming bearing in mind that this could add a lot of cost to the project.
You may find it easiest to go down the LT77/R380 route; second would be to consider the Borg Warner/Ford T5 gearbox as fitted to Ford Cosworth Sierra, Mustang and TVR - there is a lot of experience with this gearbox in competition and it is renowned for its torque capacity. None of these may have the sweetness of gearchange in comparison with the Mazda 'box but bear in mind that your Morgan is over 40 years old, has a relatively slow revving V8 but will pull the socks off more modern engines.
You may find the following link useful but note that the thread only starts at the beginning of 2017:
http://www.v8bb.co.uk/viewtopic.php?f=2&t=918There appears to be insufficient experience to comment on the longevity of the Mazda 5 speed gearbox combined with the Rover V8. Bear in mind that it is low down torque that destroys transmissions rather than brake horse power.
Finally, don't necessarily write off your 4 speed gearbox, they are more than adequate particularly if the engine is relatively standard and especially if maintained with modern synthetic oils.