I stopped at this bit. From what I have seen, the research says that the opposite is true.

There is a group called Consensus Research who look into concrete implementation POS algos and they have found that, as the work required to vote on all chains you see grows exponentially over time then restricting nodes to vote on only a single chain weakens security. As it takes less computing power to 'stake grind a better chain' (one with a better cumulative difficulty).

Their research is here: https://bitcointalk.org/index.php?topic=897488.0

I thought I would just start here before trying to look into your idea. I can get help if you have any really hard questions to ask too