I think fun is an extremely important part of keeping up the pace of learning. I would rank that much higher over "methodically combing through everything", which could cause you to quit from boredom long before you reach your goal.
I'd hypothesize that the problem you describe is due to insufficient curiosity about the way things are already done. Especially with Google, Wikipedia, and well-populated internet forums, it'd be hard not to find "foundational solutions" after a little research.
I had a music teacher who was obsessive over minutiae, and fussing about the exact position of each finger on a piano key was much less fun than loosely noodling around with chords and making things that sounded closer and closer to real music. I made little progress with the lessons and quit, but since I started noodling on my own I've been getting much farther.
I propose that "intelligent" is a synonym for "gets enough pleasure from learning to do a lot of it", so I would overwhelmingly optimize for that.
You're totally right, it's an approach that requires more motivation, but I don't think it's really that hard. University curriculums are made for young people who're not necessarily super motivated to study (many study just to finish the course, not to learn it) and who also have to study a lot of other things in the same time (and to party, and to fall in love and feel miserable and all other things that you do when you're young that are way more important to you than math). Compared to that your starting point is not that bad at all. Being older and more mature, plus genuinely interested in learning that subject you're probably way more motivated, plus you don't need to pass 6 or 10 courses that year, you can concentrate on just that one, at your own pace. Again, it's really up to ones own personality, there's no one-size-fits-all here, but IMO chances are that you'll learn it way better than someone who had that course on Uni.
And regarding wikipedia and google, they're much more effective when you know what you're looking for. If not exact name of theorem or algorithm then at least "there was that thing that we learned related to that other thing". Having at least a faint idea like that can save you tones of time when researching.
I have a lot of sympathy for this approach, and of course you learn more by having fun and continuing, then being meticulous and stopping.
However if at each fork, you choose the fun road, you might get a long way until you run out of options (which may be fine).
But the terrible difficulty is necessary knowledge that is not explicitly stated. These gaps ("mathematical maturity") are difficult to even identify, let alone fill. Story time:
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In high school, I missed a week or two, and later got stuck on a problem in calculus. Discussed it with the teacher, and he eventually seemed to see my difficulty was, but wouldn't tell me, instead saying "you can work it out". I couldn't.
Years later, I started asking online, and people responded helpfully, but didn't actually help. I read wikipedia and math websites about it. Watched videos about it, that were interesting and gave a new perspective, but didn't help my particular issue. I looked it up in famous textbooks (Spivak, Hardy), still nothing.
Finally, I did all the problems in the derivatives section of Khan Academy, but when I came to this problem, it still didn't address my specific issue.
Thinking I had gaps in my knowledge, some known to me, and suspecting others unknown, I went back to even earlier material.
Some time later, I reviewed the problem again, and realized that the issue was a completely trivial part of limits - an earlier section. Which was what I missed in those 2 weeks of high school, all those years ago.
I'd hypothesize that the problem you describe is due to insufficient curiosity about the way things are already done. Especially with Google, Wikipedia, and well-populated internet forums, it'd be hard not to find "foundational solutions" after a little research.
I had a music teacher who was obsessive over minutiae, and fussing about the exact position of each finger on a piano key was much less fun than loosely noodling around with chords and making things that sounded closer and closer to real music. I made little progress with the lessons and quit, but since I started noodling on my own I've been getting much farther.
I propose that "intelligent" is a synonym for "gets enough pleasure from learning to do a lot of it", so I would overwhelmingly optimize for that.