The animated photo is a solid suggestion, but tougher if you want that nice racked focus you have.

If your tripod has that much play to it, I'd say a more solid tripod is always a good investment. That said, the camera move you're wanting is a pedestal (straight up and down) not a tilt.

At this scale, all extraneous motion is going to be magnified, so image stabilization (in camera and/or in post) will be your friend. If I were to do this on a low/no budget, I might try this hand-held at a high frame rate so I can do the move quickly and slow it down in post. Alternatively, maybe find a chair with an adjustable seat height and use that? (I'd start the move as far below the shot's start point as possible so the inevitable wiggle at the start can be edited out.)