We had practically the same conversation today in our FS, where one of our fellows also completed the sequential quests & amassed some 1400 or so splinters and then spent all of them getting one set 1 building. Rotten luck but unfortunately there is no guarantee that you will get your desired prize - each try is independent of the others and carries the same probability of success, he did say he had a winning streak of "gain 140 splinters", 8 in a row, not too bad !
You could also try purchasing a quest package of splinters as one of our other members did. She had no problems getting the desired prizes on first or second try & often multiple times as well.
We also recommend what Killiak has suggested to choose your "target prize" in advance and to stick to that to have a "better" chance of success.
Happy gaming.