Glad to know there is some work done on PoS modeling and simulation.  I'll take a closer look.  I did some simple simulation myself.

Intuitively it will not work if all nodes vote on all chains even if you can make it scalable.  All chains will have the same accumulated stakes at the end and you won't be able to tell which chain is the winner.  I am proposing a hierarchical node structure to make all stakes participate in voting at every block height, but not all nodes have to vote - this solves lots of PoS/PoW issues including grinding.  There is nothing to grind at all.