I'm new to this forum but have been following the St. Helena saga for years. I worked on Ascension a few weeks in 1962 as an EE.. Retired from a US air carrier in 1989. I flew Convair 440's, Lockheed L-188's, L-1011's and DC-9-10,30 and 51's. The latter as Captain.
As I see the problem, it's the knee-jerk go-around response to windshear alarms that began in the '80's because of several accidents due to microbursts from thunderstorms on short finals. That is not the same as windshear at St. Helena and Funchal. I've observed lot's of YouTube from Funchal where the aircraft was clearly in an acceptable position to land and they went around. The first go-around of the 738 at St. Helena didn't seem to be much out of position either. The pilots commented that it was done because of a windshear alert. They need to turn it off at St. Helena, fly through the windshear and land 1000' from the end of the runway. Get rid of the displaced threshold and add another 10 kts. for the turbulence if you have to. The approach should be fairly predictable. Nobody's going to land in low ceilings or visibility or at night so don't fly into the cliff.
I think they should find a UK carrier to operate a 757-200 from the UK to Ascension to St. Helena to Capetown and return. There are still almost 800 of them flying. They cost a little more to fly than the A-3XX's and B-737 but they are a much more flexible aircraft. My carrier had 37 of them. When they came out in 1983, they could take off with 185 pass. on a 95ºF. day from N.Y.C. LGA 7000' rnwys. and fly against a 100 kt. headwind to LAX.