It's not Nantucket
(Maybe some googling cheater has left a clue around...)
Hello again Lone_Scout!
So, if it is not "Nantucket", then my next guess would be "Stirring Abyss
That one fits better with the "X-COM" similarity. However, I did not play it, yet. (Actually, have not even bought it, so far.) And I could not figure out its game title when I was searching through GOG.com's library for games with a matching theme.
Otherwise, I am out of ideas, and rather not take advantage of old "Google-Fu". ;-)
It's indeed Stirring Abyss.
Your turn now.