Okay, so the weather, wind, runway, traffic and fuel situations are under control. With so few flights, it's clear that the place doesn't even need ATC, even under ETOPS, so long as there's a way of getting weather information and Notams. Thus, I guess this aspect is also under control, now we're back to the original question in relation to navaids.
I'm still not convinced that anyone would be brave enough to install a MLS because, as I understand it, there's no further development going on for it. There is, however, much more development going on with GNSS navigation technology. I accept what you say about a time-out period of 2 minutes, but I'm not convinced that it's an insurmountable problem.
If the DGPS goes offline for that period of time, exactly how much adverse effect is it really likely to have? I'd suggest that the the total course deviation would not instantly degrade. It would take some time and, in fact, might only reach maximum deviation after that 2-minute period.
In any event, during that 2 minutes, the aircraft will not simply move laterally by 5 NM, in your example. It will still be travelling forward while starting to diverge from the course. I'd suggest that, if it all started to happen just as you reached a point that is 2 minutes from touchdown, you'd reach Cat 1 DA and probably still be within the required lateral tolerances to effect a landing, if visual, or a safe missed approach.
I deliberately use Cat 1 because, to me, it sounds like this place can't meet Cat 2 or 3 precision approach standards. And, of course, with the possibility of a 2-minute denegration of accuracy, the system could never be classified as anything better than Cat 1.
However, it seems to me that if you think the place can accommodate an MLS installation, then it can probably also accommodate an ILS as well. It would have a DME associated with the GP. Despite everything that's been said in the last few years, I don't see ILS facilities being phased out rapidly around the world, so this is probably going to be the approach navaid of choice.
If the place can also have a VOR adjacent to the intersection of the 2 runways, might also be able to use it to provide an alternative approach, for redundancy purposes. Thus, if there isn't much enthusiasm for GNSS approaches, I think there might be an alternative or two that would be useful.