You can have an orthogonal block chain which records a consensus on the state of the tree (hash). Voila checkpoints and debasement. Since the trees are the objective reality, then the block chain can't lie with a 51% attack. The block chain could be PoW or PoS.
Then why not use blockchain? It won't scale anyway because orthogonal blockchain will be a bottleneck here.
Bottleneck to what? It is only recording checkpoints. It is not slowing down the forward advance of the DAG. It is orthogonal, except for the coinbases which can be spent into the DAG (after sufficient # of blocks to be probabilistically sure of coinbases not being reverted by an orphaned chain).
The downside is a 51% attack could revert the coinbases, but again the DAG is the objective truth, so I assume the minority block chain can ignore the 51% attack. Would need to think this out a bit. DAGs are voting on which chain of the block chain is valid. Any way if the attacker has 51% PoW, he can attack the DAG also.