What does considering likelihood ratios of the hypotheses in your hypothesis space do to help you out here?

The likelihood ratio was for comparing the hypotheses under consideration, the Null and the alternative. My point is that the likelihood of the alternative isn't taken into consideration at all. Prior to anything Bayesian, hypothesis testing moved from only modeling the likelihood of the null to also modeling the likelihood of a specified alternative, and comparing the two.

if the truth is outside of your hypothesis space, you're screwed no matter if you're a Bayesian or a frequentist

Therefore, you put an error placeholder of appropriate magnitude onto "it's out of my hypothesis space" so that unreasonable results have some systematic check.

And the difference between Bayesian and NHST isn't primarily how many assumptions you've committed too, which is enormous, but how many of those assumptions you've identified, and how you've specified them.