You might also try taking it from further back, and cropping out the part you don't want. Sometimes it's easier to focus that way and you end up with less distortion. Putting a dark card in will help, just make sure it's on the far side of the inside of the tumbler so that light can get behind the cutting. It makes gray cuttings much easier to see.
I've been experimenting with putting water into an engraved glass to take a photo of it. I've had some good results.