I think I’m beginning to understand your use case a little better - it’s not so different from my own. The main difference is that our helpdesk team only has about 5 people in it (goes up and down throughout the year as staff come and go) and otherwise we discourage the use of discourse group messaging for everyone else even our staff of 150+. For those we use private categories. We also invite specific colleagues from time to time in messages to get help responding to helpdesk messages.
The reason for this is that people tend to confuse discourse group messaging with email - even though it is similar it is different enough that people get confused and even a bit frustrated. That said, group messaging is improving and I am understanding better how it works and what it is good for, so maybe at some point we’ll expand its use in our organization.
Recently I delegated the helpdesk to colleagues, and changed my own notification level from watching to tracking. Watching turned out to be a bit much - once you get more than a few people responding to group messages your notifications (and maybe your head) will explode. 
Now I make a point of looking in the group inbox and archive once or twice a day, and look for the blue dot next to the messages I haven’t seen yet - works great. I can spot check the messages and add any follow up that might be needed. My colleagues might mention me in a whisper or assign a message to me and then I can respond more quickly. They can also add more people to the message and ask them to respond.
Since you have 100+ people expected to monitor the group messages, you could also have them track the messages and remind them to look in the archive.
Another idea would be to create some more groups to separate out the people who are doing most of the answering and archiving. 100 people is alot to have in one group anyway if you want them to feel accountable and engaged. We have one “all staff” group of 150+ and only really use that for announcements and to give access to a few private categories.