The run configurations let you check a box that drops you into the interpreter console afterwards. If you install iPython, it will be used. Is that describing what you're looking for?
Not quite. If you re-run the script it creates a new console rather than restarting in the current. That leads to an awkward proliferation of consoles with no keyboard shortcut to close them. I encourage my students to run code very frequently.
I'm hoping I simply overlooked something.
You can tell PyCharm to only run a single instance of python by going to Run -> Edit Configurations -> Tick 'Single Instance Only' in the top right.