I have done research online and there seems to be several different CX map structures.
Some have steps at the top and then touch points along the left.
How do I determine what CX map is suitable for my scenario?
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The best way to go about this is ask yourself what type of story do you want to tell. You mention touch points on the left or top, but neither really makes a difference. In the end it depends on what type of story you want to tell and how much time you want to put into it.
I have seen comic strip journeys and journey maps. The only real measure of success is ensuring your audience will understand what it is your showing them and seeing its value. Following a format design for a different experience is probably not going to yield the best results. I prefer to start with a sketch pad and try to illustrate the experience to myself. Once I'm done, then I start to put something on screen.
In the end, it's up to you, because you know your audience. Come up with something creative and entertaining and you can tell them just about anything.