You almost certainly need 2 nests and 2 breeding dens to get far in the event, but maybe they place you with other players who also only have 1 of each if that is your situation. I don't know.
If you can't spend any gold at all, then I don't know what to advise. If you can spare some gold, though, I will tell you that I use a boost every morning because over the course of the night I usually have things finish breeding, incubating, and evolving - or use gold any time I have all my stuff ready to go at once. I also use an evolution boost and a leaderboard boost when I get the common dragon we are breeding for. Since they are only 4 hours at a time, I use an evo boost and only have to spend 3 gold to get it to level 10.