Not relevant to actually getting the 3rd UHV, but to get your score as high as possible you have to be strategic about buying techs. Sort of stupid and pointless, but you may have to S/L to see the appropriate techs you can buy before you "become too advanced." Basically, you would need to buy enough techs to reach the "too advanced" threshold minus 1 tech, and then on the next turn buy as many as possible. Again, stupid, but if you want your inevitably low score to be slightly higher, it's the way to go.
Finally, at some point of expansion, you're going to want to avoid new techs, as not to trigger a stability check.
Now my own question: is it possible to eliminate the clouds and show the detailed game map beyond the default... zoom-out level (or whatever you would call it). Like, if I wanted to get a detailed screenshot of all of South America, is that possible?