I'm not as familiar with Zoom as Discord/Twitch/Youtube...

Of those three, I'd use Discord for voice chat, map, and screen viewing, but it doesn't support streaming from your camera. SOoOo, here's my take:

Discord lets can host your own private server, with each voice channel hosting 10 people watching a live stream. You can also create text channels to chat outside livestreams or place interactive games/links. Discord is what you're looking for in terms of a top-down, white-listed (or graylisted) approach. Creating and maintaining infrastructure of a Discord server is VERY straightforward. Another great benefit is the bots people have already made for Discord that could suit a variety of needs. For example, music bots are great for voice channel rooms where there are no live streams going, but people want to listen to music and chat in text channels (or have the music softly playing as others talk). It'd serve as a great place for the map you're looking for.

As for video chats, Zoom is where I'd put my money on, and Twitch for shows. Twitch does everything you'd want out of YT livestreaming, but better - it's what it was made for. Discord was made for internet socializing, featuring a damn good voice option.

TL;DR, Discord can work as a great nexus. A private server containing links for each show in chat/voice channels general voice/text hangout which can also serve as general chat/music/voice/screensharing hub.

As always, there could be options out there that are worth exploring. Facebook Live, Mixer, and others.