I always thought this was unnecessarily made to sound counterintuitive, and I think there is a way to explain it simply without trying to make it sound like rocket science.

Instead of "speed up to slow down", it's "speed up to go higher". I think anyone can get on board with that. You'll come back to the same point you were when you accelerated, but later than before since you went into a higher orbit.

I like the included animations, since it also makes it clear that accelerating or decelerating from a circular orbit makes it elliptical. Your don't just jump to a higher or lower circular orbit.