We have new people moving in and out quite frequently in our team and only years after we recognized a value behind some sort of an on-boarding guide for all new people in a team. We don't have a huge code base but the complexity of the environment and final seemingly simple solution is often hidden and not openly stated anywhere. People don't write explaining the reasoning behind even most important details. Even the final solutions are usually described verbally to stakeholders during the meetings. What to do if stakeholders didn't get it during 1hr meeting or forgot everything since the last 1hr meeting, well then just setup another 1hr meeting.
I'm trying to show by example but it seems like it's not working. I have an impression that it's just the trait of OG people in our team. When I get pissed off when I waste my time in meetings/communications, others just accepted that as a permanent state of offers: yep people ask me questions and I have to answer them, there is nothing I can do to change that, well I can spend 10 minutes writing the answer once and for all, but no I will spend 3 minutes just answering it in an email/messenger/call now and hope nobody will ask me that again and don't ask me what is going to happen if I quit.
I too have been in your situation. If there is a solution to your immediate problem, it is one which requires as little exertion or deviation from those already involved, and one which addresses your ultimate concern… a culture of knowledge which may be reflected upon in time of need where ever the colossal requirements of your work falls upon any one of you to handle its’ exceptions.
In an age threatened by automation, let our exception handling set us apart!
Practically, your screwed. I have empathy for your passion. Abandon ship, in ten years you will be a greater Man who will simply not repeat this problem.
For now, if you went “occult knowledge management” (yes, been there.) you must through will assert among disparate interests using motivations only equatable in benefits to minimally participate in workflows capable of capturing such knowledge as you seek.
This knowledge must be processed. An additional individual (or “core” depending upon how committed you are) will be required. You may not delegate this new burden upon any who is not chiefly rewarded for its success.
Good luck. Despite mass layoffs, true skill and passion for knowledge integrity is ever lasting.