Your fallacy here is in thinking that "people with much less talent than myself are considered stronger musicians just because they know the "right" fingerings?"
Listen more closely to what you have actually been told: "they say that the fingerings are an absolute must." Unless you've left something out, they never actually said you are a worse musician for not employing the expected fingerings.
Now, consider the possibility that they are not saying that to you because students who know and employ the standard fingerings are better musicians than you. Perhaps it is simply because they will make better students for that school.
You are applying to be taught by these institutions, at great expense to yourself and indirectly to them, and their classrooms are staffed by instructors whose entire body of knowledge is built upon that standard foundation. In order for them to instruct you most effectively, they need to have a shared frame of reference with you.
When there's a shared agreement about the basic approach, they can focus their attention on more advanced refinements and enhancements to your technique. When there is instead a fundamental disagreement about the basics, the instruction can be sidetracked over arguments about whether your idiosyncratic fingering is more or less effective than the standard. You will likely end up learning less than another candidate, simply because you are not immediately compatible with their pedagogical model.
Now, if you were to say it I would agree with you that the established pedagogical model is not necessarily the best one. It is entirely possible that there are alternate approaches that are more effective. For example, for many years we have known that the Dvorak layout on a typing keyboard is more efficient than the standard QWERTY, but everyone is still taught QWERTY as the standard. And with good reason: the vast majority of the keyboards in the world are QWERTY, so even if the dusty old pedagogy is dated and inefficient, it does make you immediately compatible with the world at large.
The same is true of musical pedagogy: it has its crufty corners, but it still prepares you very well to be compatible with the classical music world at large. If that is something you aspire to, then you're going to have to be prepared to bend your will a bit to accommodate the imposing weight of the classical tradition.
On the other hand, if you are more committed to remaining unconventional, seek out those schools that will support you in your idiosyncrasies, and lose no sleep over those other schools that won't. In communicating to you their insistence on conformity, they are merely doing you the favor of steering you more swiftly to where you truly belong. Thank them for it, and move blithely on.
