Peter J - you make valid point about the MX5 gearbox in the Threewheeler application. That V twin will put the transmission under some stress. Also, the subsequent link has been revealing too.
Rory, my memory as jogged by looking back through some old messages.
For what it is worth, I will give you my thoughts but they are out of step with the bulk of advice that others on TM are giving you. Firstly, because I own older generation Morgans rather than new generation ones but also because I have worked extensively on them for 40 years that has included rebuilds and race preparation.
The car is yours and yours to do with as you see fit. However, I feel that the car, particularly given its chassis number, deserves some careful consideration. If it was a Moss gearboxed car, I would definitely suggest not replacing the gearbox as that car's narrow stance and Moss gearbox are part of the car's charm. The 4 speed Rover gearbox has a bit of a reputation for being weak but remember, what gets printed in a classic car magazine ends up being total truth regurgitated by 'enthusiasts' with clean fingernails.
Changing the gearbox will attract associated additional costs including recalibration of the speedometer instrument. These can add up considerably.
Once again Rory, the car is yours to look after and modify as you see fit. Just bear in mind that advice that simply tells you to "change it" should be treated cautiously.
Finally, I have shared recently a full set of sketches for converting a Plus 8 from a Rover 4 speed to an LT77. I am happy to share these with you if you wish. They were given to me by a fellow Norcemog member decades ago (his car was recently sold at the Bright Wells auction) who converted his car. I used these sketches and measurements when I converted my car.