The only way to resolve this is to have centralized servers which are trusted to cooperate and organize around a single chain.
This looks bold to me.
Feel free to point me to any publication that will explain to me another way of doing it. Since you are about to launch, I assume these details have already been sorted out and thus you should have no trouble providing the details.
I will certain mea culpa if you have found a solution. But I am 99% sure you have not. Once you provide the detailed publication, I can zero in on detailing to you what is your flaw. Or mea culpa if you've discovered something I didn't anticipate.
Note the above quote is a simplified way of stating the many possible ways I've analyzed how a DAG might work, so even if you are doing something slightly different from your pespective, I think I will have already considered what you are doing (I didn't want to write a book here).