My feelings on this are very similar; Looking at my competition in trying to enter grad school from industry this past year has me awed and feeling totally outclassed (partially due to the increased field due to covid) - undergrad publications, completely flawless academic records, awards, recommendations from famous professors, etc. By compare, I'm just some mook from a small state school with average grades & good test scores.

Perhaps I need to be more willing to make certain sacrifices, since it's increasingly clear so many do. In that respect, I'm deeply humbled.

I’d encourage you to just apply to some good programs, don’t get psyched out by your perceptions of the competition.

Grades, papers, recommendations are all important, but they’re not everything. There’s a certain randomness to the graduate admissions process - different departments have differing values and priorities, and often the graduate admissions committee is different year to year. Many departments just use grades and such as a heuristic to help narrow the pool.

A demonstrated ability to write well (put time and care into your statements) and think independently count for a whole lot.

I'm more or less going this route. My current plan, if I do strike out completely, is to enroll non-degree near my hometown and build some credentials & relationships in the local department while working. It's a top 50 Mathematics program, so it should still provide what I'm looking for.

There is no single measure of intellect. We as a society just set some arbitrary goalposts and added some ways to measure contribution. The ability to take a step back and try to better understand reality will always be valuable, and there will always be a horizon there that we cannot measure.

Measuring intellect is one thing, valuing it is another. Within my lifetime I've sadly seen intellectual excellence valued less and less by society with each passing decade.

I see that intellect is valued more and more intensely by a smaller and smaller group of people. I'm not sure what that means, but it gives me some small hope.

Best bet is probably something like cern or quality physics/math/philosophy faculty at a university somewhere

I kind of gave up understanding relativity and quantum physics, but might try again later.