I think the best response to the argument for instrumentally useful false beliefs is to think a little about the causal mechanism. Surely it is not the case that Omega reads your minds, sees your false confidence, and orders you hired.

As you noted, a more plausible mechanism is that the false confidence causes changes in affect (i.e. appearing confident) that are beneficial for the task. Or perhaps false over-confidence cancels false under-confidence that would have caused anxiety that would be detrimental for the task.

Once the causal chain is examined, the next thing to ask is whether the beneficial intermediate effects can be caused by something other than false belief. If so, you have answered the claim you are responding to. If not, examining why one doesn't believe it possible needs to be examined.