> The "balls on a rubber sheet" is a pain because nothing is in free-fall

The balls on a rubber sheet model is actually really great, but not in the way it's typically presented (rolling a ball down the curvature). Instead, just use a pen to draw lines to show the concept of geodesics.

Start like this:

1. Imagine that you can move without friction if you stay at the same vertical level.

2. Draw a line on a flat rubber sheet, that's a line in free space. It's just a straight line that can go on to infinity.

3. Now put a ball onto the rubber sheet, so you get some curvature. Now the lines near the ball that stay on the same level are not straight lines, but circles.