Show reply link on hover instead of all the time.
Instead of showing the "Reply" link at the bottom of every message, the link would only appear when hovering... like Slack's thread feature.
Sean Ellis commented
I think the problem goes deeper. This is a classic case of trying to go against years of ingrained behavior. Pretty much every other chat application uses a text box at the bottom of the screen to continue the current conversation, not start a new one.
By sticking to this established convention, the need for the "reply" buttons disappears and "Start a new conversation" becomes the special button.