It's even easier than that -- all you have to do is get a stake and then brute force mine for an alternate reality where your stake is the sole decision maker for the DAG.

You can't really double-spend that way, but you can get a disproportionate amount of the shard rewards. In order to defend against this, other participants will also have to mine for a "more fair" alternate reality, so you end up getting a standstill where nobody can get economic advantage as long as the total power being devoted to preventing chain-shopping is greater than the amount spent on chain-shopping.

In the end the energy expenditure would likely be unchanged from the status quo, it would just be hidden behind a facade of inexpensive proof-of-stake validations that conceal the actual work being done to ensure that this is not abused. This way everyone can feel warm and fuzzy because there's no actual way to measure how much work is being done to keep the validation from being monopolized.