Have you been trying for any other daily prizes?
Generally speaking, if you want a full set, then you should NOT! be spending any moonshards except on those days that have a building from the set you're after as the daily...
I've been going after the 1st set myself, as I'm a strictly 'no diamonds' player.
By sticking to the small 50 shard chest, I've completed the full Day set + 1 additional entrance building so I can get full boosts from a couple of the main central buildings, and I've still got 2300+ moonshards left! (I even managed to snag a pair of the Burning Man culture buildings on day 1, but that was just sheer dumb luck.)
Honestly, I've found that I win more dailies when sticking purely to the 'small' 50 shard/acorn/snow crystal/whatever chest, since you'll win a metric gak-ton more 50/90 moonshard prizes & thus more attempts in general at the chests.
Especially on the double days, you can really clean house outside of extremely awful luck!