I understand the necessity of the Jewish State, but I am asking if that necessity forced us to go over the specific prohibition of forming a secular court system.

The answer l'chatchila is that of course the court system of any Jewish State should be according to halacha. Nevertheless, God "has to" deal with several givens: Given 1: God gave us free-will. Given 2: Most of the Jews in the world have unfortunately "willed" over the last century, for the time being, not to be religious. Given 3: God promised our forefathers that He will redeem their children, and the redemption (ge'ula) is for all Am Yisrael, not just for the religious. Given 4: If so many Jews remain secular outside of the Land of Israel, they will soon assimilate and be lost. There had to be a secular Jewish State which would be "relevant" to all these secular Jews. The God of History can solve any problem, and here did so through the unfortunate (but apparently necessary) historic reality, that nobody, not the British, and not the secular pioneers, asked the rabbis how to make a court system that would be relevant to most of the Jews. They simply didn't ask (see similarly Sukka 43b). Rav Kook put it this way: "The b'dieved of man, is the l'chatchila of God", Who runs the world. On the other hand, as I wrote previously, we are still in the middle of the process, which is already seeing the gradual spiritual strengthening of Am Yisrael in Eretz Yisrael. The rate or speed of this process, depends on our actively bringing all of our brothers back to Torah asap.