The Moral Imperative Towards Cost-effectiveness
I enthusiastically agree with most of your ideas. This is a very insightful text. However, I partially disagree with your paragraph on Cost Benefit Analysis ("Another reason people might be initially suspicious of prioritisation based on cost-effectiveness is through confusing it with cost-benefit analysis (CBA). [...] the wealthy are willing to pay more for a given benefit.").
Willingness-to-pay is a measure of subjective value relative to the marginal utility of money. Indeed, "the wealthy are willing to pay more for a given benefit", because marginal private consumption provides less utility to a rich person than to a poor one. Therefore, to use CBA in a more ethically acceptable fashion, one would need to adjust benefits (measured in dollars) according to marginal utility of income of people receiving those benefits.
Even though that practice is still relatively rare, it is already mentioned by British and French guidelines on economic appraisal. I don't know much about how CBA is done in the US, but anyway accounting for the diminishing value of the extra dollar is not an intrinsic limitation of economic appraisal techniques. Those techniques do have some other drawbacks. On the other hand, they can also overcome some limitations of Cost Effectiveness Analysis. But that is outside the scope of this comment.