4 minutes seems like a fast bake for a home oven, specially with a thicker crust. How hot does yours get ?
That is too much char for me as well.
A couple things you can do...
You can bake on a pizza screen.
Bake at a lower temp for longer time.
I was going to suggest using the oven with broiler on to get top done sooner, but I don't think that would help the crust any.
Baking in a pan could be another option.