It's more important to give people some mental picture than to make sure it's completely correct. But, I would not use the "slope" terminology. The important things are, as you've said, (1) with the complex type, you can have a signal at baseband that is not symmetric, and (2) the price for this is doubling the amount of data needed. The signal you deal with at baseband is the same signal that is seen centered on the RF carrier.
I don't see a great way to talk about "phase" without going into the math. It is important to get into "phase" when you talk about any modulation fancier than slow FSK.
Good luck. Hope you find the right balance between useful, digestible, and correct.