Solution: I chose Hellman's Mayonnaise, and decided to use a knife as a prop since it would be fairly simple to make and it is a utensil commonly associated with Mayo.
I began with the parts of the jar actually showing mayonnaise. I would pick which part I wanted to work on, trace around it with the pen tool, fill the area with the general color that it would be, then use the gradient mesh to adjust. To achieve the highlights and shadows, I would put mesh points within the areas themselves, and then place more around it to control the degree to which it spread.
One of the first things I did was trace the largest letters on the jar, just to get started. I used no mesh on the letters, mostly because the odd shapes messed with the way the mesh formed. For drop shadows, I just copied the letters and positioned them correctly, then color-picked the shadow behind them. The hardest part was tracing the obscured words on the top of the lid, as well as on the bottom left. The ones on the top could be reduced to general shapes, and it looked just right. The words on the bottom right, however, could be easily read when printed out so I had to continually zoom in, adjust, zoom back out and repeat in order to get the letters looking as normal as possible.
One of the biggest challenges was making the swoosh on the label look right. I tried to just use a gradient mesh and fade the edges into the yellow with the color picker. However, no matter what I did, the swoosh always stood out too much. Eventually, however, I decided to pen-tool the shape, use a gradient to get the movement from a lighter gray to darker, and then use a feather effect so that it would fade into the yellow like it was supposed to.
The other most challenging part of this project was the shadow in the background. I had problems similar to those with the swoosh, the shadow just stood out too much on the edges. I eventually decided to go with a solution similar to what I did to the swoosh. I pen-tooled the shape, used a gradient mesh to get the colors inside of the shadow correct, and then used a feather on the edges so that it would properly fade into the background.
For the ridges, I just made rectangles approximately the size of each ridge and copied them all along the lid.
One of the last steps before the finished project was making sure that there were no empty spaces between the pen-tooled shapes. To see them, I just took away the background, and adjusted the shapes to fill any gaps that weren't supposed to be there.
Here's the finished project (followed by the original, again):
