Might I suggest either speech text coloured based on who is talking or more variety in how you say somebody is about to speak.
For example: He gives you a surprised look, "Nah, not human. Born from an egg and everything."
As long as you mention some kind of action or reaction by the person about to speak it suggests they are the one speaking, by having some cases where you outright state you say, "" but using emotions or actions leading to speech to add variety it makes conversations more engaging to read than a chain of he says"", you say "", he says "".
On the text colour approach you don't need to say anything to show who says what as that is identified by the text but mixing in descriptions of peoples actions helps add emotion to a conversation still and looks better than just a colour changing wall.
I hope that made sense and the feedback is useful