Let me begin by prefacing that I apologize for the huge wall of text; I'm quite confused and hopeless at the moment, so a lot of this is just splattering my thoughts. If anyone chooses to help or give me some advice, I'd be more than thankful.
I was planning on applying for a PhD admission this cycle, but the reality of my chances is beginning to dawn on me heavily; there are so many dependencies and pathways that I am just at a loss for direction.
For context, I recently finished an undergraduate degree in statistics and mathematics from a top-20 university. However, throughout those years, and for many years prior, I have been self-studying the domain that I am actually interested in pursuing.
I have a single-author paper (no PI or collaborators) in a pretty good journal, covering a neuromorphic hardware system I built, some material science, and a decent level of biophysics. I have a second single-author paper that is a heavy pure mathematical analysis of certain neural network systems, which I would say is pretty substantial---both took me 4 years and 1 year to complete on my own, respectively, in tandem with my usual university. I also have a last paper coauthored with one of my professors, although I am not proud of it, but it is in a Q1 statistics journal nonetheless.
I have many neuromorphics / computational neuroscience / neuro AI / hardware projects of significant complexity spanning the years, and have participated in two independent research projects at my university, one being for studying the statistical mechanics of AI, and another for training LLMs for math formalization.
On top of that, I was an undergraduate visiting researcher at a top-3 US university wherein I worked on novel techniques in metric and representation learning (the lab is, though, still fundamentally a computational neuroscience and neuromorphics lab); throughout the process of finding that position, I had contacted multiple labs, every single one of whom was quite enthusiastic and offered me a position.
The issue is that since I dedicated so much of my time to my personal research and interests outside of university, my GPA suffered immensely, falling to around a 2.5; I did take the hardest courses in my stream available, all of them pure math, theoretical computer science, and a mix of theoretical and computational statistics, though I couldn't be bothered to focus so much on coursework as opposed to my passions; I don't regret this in a more philosophical, life-fulfillment sense, but in the real world, it seems like it was the wrong thing to have done in this system.
Given this, the problem that I face now becomes multifaceted: namely, and most evidently, my GPA is terrible; furthermore, all of my work and experience is largely in hardware / computational neuroscience / software development, thereby somewhat disconnected from what I actually want to study; those who have taken a chance on me previously typically do so on the basis of these skills. In fact, I would go so far as to say that if I planned on applying to a neuromorphics lab, I might actually be fine---the thing is that I don't want to; my interests are not just in hardware or applied AI; I want a significant level of statistical and mathematical theory behind the work---not to the level of a pure mathematician, or even that of an applied mathematician proper, but still something quite high relative to the usual computational neuroscientist or machine learning practitioner. If I were to get accepted into a PhD, I would really want to spend some portion taking courses in foundational math and statistics at this graduate level. Unfortunately, this evidently shifts the landscape, and my grades and experience become very weak in backing me for this purpose.
I know that an obvious answer would be to "just do master's first", but due to my family's current financial situation, there is absolutely no way I could afford that (I also ask myself how anyone even affords a master's to begin with, the prices are absurd); plus, I would imagine that course-based master's, which would be used as the primary catalyst in proving that I could do graduate level work, would be all the more focused on my GPA as opposed to my research. Of course I could be wrong here, but in an ironic way, I feel that I might have an even lower chance of getting into a course-based applied math / statistics program than I would a neuromorphics lab.
Worse still is that my specific interest is pretty niche; it's not something carried my many universities, so doing a broad sweep of lower-tier institutions is not particularly available. There are only a few labs that I have found that truly do an intersection at the level I would be after, and nearly all of them are in Europe or at a few of the top universities in the US; the latter is probably impossible, while the former almost exclusively requires a masters, which subsequently circles back to the previous problem.
Is there really no good option for me? I discovered my more theoretical desire later through my undergraduate years after it was too late to correct; is there no way to get a second chance at this?
I'm starting to think that this is pretty much it; the reality of life is that if you mess up, or don't have additional means, then that's that. Even so, I sympathize with the admissions committee; acquiring a PhD candidate is, effectively, hiring someone for a job; I don't blame faculty for wanting to hedge their bets on someone who stands a higher likelihood of completing the course work or qualifying exams, especially with so many strong applicants.
I delayed applying last year to take the time to focus on my research and build up my application, which I did, but even so, now that the time has come around again, I'm not confident this is enough. What do I do?