Welcome to our Support Community. Thanks a million for creating such a detailed post with info on the steps you've already tried -- it's super helpful! The only other thing that I can think of would be to delete that specific group and re-create it to see if that does the trick. Usually when you restore your iPhone, all of the messages are restored as well if using iCloud. If that doesn't do the trick, I'd recommend you work with our Tech team to file a ticket with our Engineers. That can be done either via 611 or by working with T-Force over Facebook/Twitter.
I am having this same problem, I have tried all the same things you tried.... any tips on what worked for yoU??