I feel like there should be a way to internalize those arbitrage opportunities, rather than wait for 3rd parties to do it.

For instance, let's suppose for simplicity that about half of the liquidity is on the 49ers and the rest is spread evenly across all the other teams. If I buy enough shares that the 49ers would move 2% in a single market, they would now only move 1% and every other team would move proportionally to rebalance the cumulative odds.

I'm thinking about it like a physical balancing act, where liquidity is analogous to mass.