> I'd like to understand more of the problems we're facing so I can participate in the discussions.
There are two very different contexts for "discussions about security" in large enterprises.
1. discussing security with management / C-whatever
You need to discuss risk. You must show that there are some things which are important , and other less important. This is not an easy discussion because it requires experience and the ability to say "if this is hacked, never mind" and at the same time fight like your life depended on it to have the small XSS on your corporate site fixed. Not because it is insecure but because it does not look good in newspapers.
You also need to discuss awareness. First for them, then for the rest of the company. Because the weak link today is John in accounting who will open the enlarge your penis email end download the attached binary.
→ it is difficult to find good resources to learn about these things. Of course there are zillions of books about the subject, usually written by people who have never actually ran the security of a company. At best they were "consultants" who had great ideas, which were unfortunately in another galaxy realism-wise.
I would say the best would be to have the opportunity to work with a good CISO and watch him or her belly dance to make their point with management. If they are good you will quickly understand what is important and what is not.
2. discussing with technical teams
You can expect a competency ratio of 1:4. That is 1 person who knows what they are talking about for 4 others who are either neck deep in technical problems and need to solve these problems, or the ones who learned security as part of their general systems/networking curriculum.
The best way to integrate such a team is to become a jack of all trades a master of all trades as well. In technical teams, raw technical knowledge counts a lot - especially in technology companies. You get credibility points exponentially when you help to solve a hard technical issue. Best is to look around authentication, machine to machine traffic (and how to secure it) and application security.
→ best is to try it out yourself at home. You can run a docker server on a home server and start a few containers. Play with authentication, automated TLS, reverse proxies and filtering, logging.
Large enterprise security, technically speaking, is either the same as small enterprise security (multiplied by n servers and services), or really specific (peering, centralized authentication, ...). The first you learn at home, the second you learn by reading about that very specific subject on Internet.