What exactly are you looking for? A replacement messenger or something that allows communication with those messengers?

Threema sadly blocks api access behind a paywall and community interest isn't high enough to have resulted in a workaround using the regular client access.

As for the main request, it is probably a bad idea to move to messengers as the primary communication tool. I would rather suggest to look into a tool like Loomio that has nice notification options to link the decision making process to various chat apps.

What about something xmpp-based like Jabber, Prosody, or Snikket?

@MicKet @selfhosted Matrix or Mattermost maybe.

XMPP with slidge is what you are looking for. 

Have you checked https://awesome-selfhosted.net/? 

Mov.im ? A web frontend for xmpp. Though it's not hostable via docker (there is one but not for production).

I'm not sure it will 100% suit your use case but definitely a solid choice.

If they're already using Signal, why not use that, instead of trying to get them to install and set up yet another app?