Seamless background...

How could I improve? Thanks in advance for any tips.

You could improve to an 85L.. hehe

I'm not a product photographer but it looks like it could use more fill light.

I found that you can get rid of (or decrease) the off white background by going to Photoshop, creating a Curves Adjustment Layer, and setting the white point at a spot in the backdrop that is the least white. I spent one minute and got this:

HTTP response: NOT FOUND | MIME changed to 'image/png'

I'm not at all an expert but I think it looks good. You have everything in the depth of field, the only thing missing is the 1.4 so you can fully identify the lens.

I need to calibrate my monitor... The background has an unappealing purple tint on my laptop but a nice gray on my phone.

First one yes, not completely white, the second one (on my monitors) is white.

I think it's a pretty good image. I did look at the Canon site to see what they do and they almost never shoot facing the lens. The couple of images that they do use have the area in the lens uniformly soothed out. You might look at some of the other lens manufactures to see how they portray their lenses. If your goal is a professional lens shot than mimic the pros.

Charles