ROBLOX has recently introduced a Group Shout/Status Update API. Credit to @EchoReaper for the suggestion.
If setting up a proxy to receive requests and shout using pre-made libraries isn’t your thing, you can use this to post updates to your group shout by sending a request to the URL below. The request body should contain a JSON object with the key and value respectively: "message": "string_to_shout" The request method is PATCH. More info about the API can be found here.
https://groups.roblox.com/v1/groups/{groupId}/status