A couple years ago we had an amazing all-star session at the Joint Statistical Meetings. The topic was new approaches to survey weighting (which is a mess, as I’m sure you’ve heard).
Rod Little combined design-based and model-based survey inference.
Michael Elliott used mixture models for complex survey design.
And here’s my introduction to the session.
At slide 16 of your intro, the weight for men should be 48/40, rather than 40/48, right? Since men are under-represented in SRS 2.