OK I created the following Matlab code:

Cool!

The plot isn't very impressive. It looks like a line straight through the center. The min radius is 114m so basically over 6500m drop the center moves about 114 m.

That doesn't seem right. You are doing the calculation in the rotating coordinate system of the Earth?

Equatorial rotational velocity of the Earth is 465 m/s. The center of the Earth is stationary in the rotating coordinate system, so over a 22 minute drop, the lateral displacement should be 614 kilometers. That's not the distance by which you miss the center, since as you deviate from the initial radial line the gravity vector changes direction, but the effect of that will be small until you get to distances that start to be comparable to 10% of the Earth's radius, so it should be close to the miss distance.

It's a non-Keplerian orbit (even in the non-rotating frame), so you don't come back to the same place you started.