What would be the aims of your songwriting group? If to compete, I don't think you will find it works very well. I co-host a songwriting group that started as an experiment and is still going strong after 18 months and so far, so good. I am really happy that it seems to be working so far.
However, we do not run it as a showcase for our own songs, but as a supportive and friendly social group with egos left at the door. It sounds a bit pretentious but we were determined not to have some taking it over.
We all write in different ways so I don't think you can tell someone how to write songs but I think listening to others keeps you more open minded.
Songwriting is a fairly solitary thing but we find it is good to share our ideas and pick up ideas about how others approach writing. None of us take ourselves too seriously and I can honestly say I think each one of us has benefitted from the group in various ways. Some of us like to use themes to inspire a song, others just prefer a freer approach, writing about anything that just happens to feel worth expressing in a song. Some use all sorts of approaches.
I feel I have made some new friends who understand what it feels like to complete a song you have written and developed yourself.
I hope if you get a group going, it is a positive experience and that a non-ranking supportive atmosphere is achieved rather than a few forceful, (notice I didn't say 'strong' as I mean 'loud' rather than strong) characters taking over, who like the sound of their own voices too much. Best wishes, and probably a good idea to have a single identity name rather than 'guest' as above.
PS One of the group even stated that it has totally changed his life...in a very good way. That is worth a great deal to me.