We have a lot of really smart people working from that approach already

We do? Like who? There are qualified people who don't work on the problem, and also a few unqualified people who do. Maybe six people I know of who are both qualified and possibly do useful work on the problem.

But I feel a lot more comfortable playing around with concepts like timeless trade than recursion theory: probably because my weaknesses are less apparent there, but still.

It's a matter of improving your sanity when thinking about conceptually difficult questions, not of narrow skill or "approach" (which is a weasel word, like "in my opinion", trying to lift responsibility). Anybody smart can study.