I spent some time on DAG based designs and this one reminds me of something that I rejected early.

As far I understand, the level of security against double-spends basically depends on the total amount spent on fees on the legit DAG.  If so, an attacker just secretly builds a subDAG that includes a few double-spends, spends more on fees in the subDAG than was spent in the legit DAG, then publishes his subDAG.  Now everybody should switch to the subDAG as it has burnt more fees.  As long as the total amount of double-spends exceeds the fees, the attack succeeds.