The problem is that if we accept the possibility that we're brains in jars, the vast majority of our information becomes unprovable.

Yes, this can occur from believing the answers to unanswerable questions. This isn’t unique to the philosophical brain in a jar scenario, it’s applicable to practically any question that is unanswerable. Basing logic on the answer to an unanswerable question leads to rabbit holes.

I can't disprove the strong skeptical hypothesis, therefore I can't know anything that would be disproven by the strong skeptical hypothesis.

What happens when you try to prove a proposed answer to an unanswerable question? Why try to prove or disprove the “brains in a jar” scenario when it’s unprovable? Do you accept that some questions are unanswerable and that the answers to unanswerable questions are unprovable?

What we know is multi-factorial and begins on a subjective level with sound parameters and practices (like repeatability and other scientific methods) and is confirmed or verified on a shared level. Unprovable scenarios like “brains in jars” can be suggested and can reveal more about unprovables than it does a commonly accepted truth in a commonly accepted shared reality.

I don't think it's an either/or between belief and knowledge. After all, anything I know is also something I believe.

If it is your agenda to say that you believe all that you know then this is just your perspective. I know that I have 5 fingers on my right hand. If you understand and accept the meanings of the words “I have 5 fingers on my right hand”, we occupy the same space in commonly shared reality, and you exist on a human wavelength then upon proving to yourself that I have five fingers on my right hand this information would become knowledge to you without requiring belief. And yes, even then if your agenda is to base all you know on belief then you can do this and I cannot disprove what you believe nor your ability to believe. But then this just says more about you as a person than it does me or commonly shared reality.

What I'm proposing here is that we can have solid justification for holding a belief even in absence of knowledge or proof that the belief is true. On the brain in a jar scenario, I'd say that I can't disprove the hypothesis but that I don't have justification for believing that hypothesis. Between the positions of belief and disbelief, I think that the reasonable position here is disbelief.

People can and do believe whatever they want to, and what people do believe is usually aligned with their bias and agenda.

If I premise other beliefs on this non-knowledge disbelief of strong skepticism, I'd similarly say those beliefs are not knowledge, but nor are they just things that I happen to believe. They're "reasonable beliefs": the most reasonable positions I can take given the evidence I have, even if I don't possess knowledge.

They are unprovable regardless of reasonability.