We were able to get KeenTools licenses which makes it much easier to handle the logo replacement for the last two shots of our spot.
I started by creating a cylinder with the same measurements as the real jar. I then used the KeenTools geometry tracker to track it into the scene. To replace the logo, I had to paint out the old one and put the new one back on top. The easiest way I saw to approach this was to stabilize and flatten that part of the image, do the work there, and redistort it back. This can be done by projecting the footage onto the tracked geometry and rendering it with a ScanlineRender with the projection mode set to UV.
The result looks like this:
Here is the plate and the new logo tracked in. I am still working on integrating the new logo with matching the shadows and rebuilding reflections.