Secondarily, you are the first person to give me a solid reason as to why the current paradigm is unworkable. Despite my mediocre recall I have spent most of my life studying AI well before all this LLM stuff, so I like to think I was at least well educated on the topic at one point.

Unfortunately it seems that your education was missing the foundations of deep learning. PAC learning is the current meta-framework, it's been around for about four decades, and at its core is the idea that even the best learners are not guaranteed to learn the solution to a hard problem.

I am somewhat curious about what architecture changes need to be made to allow for actual problem solving.

First, convince us that humans are actual problem solvers. The question is begged; we want computers to be intelligent but we didn't check whether humans were intelligent before deciding that we would learn intelligence from human-generated data.