OP here. Thanks for the comments. I'm glad I'm not alone, but this is definitely frustrating. We had a dog before this that never did this, and I grew up with dogs and never had one of those do this regularly (except one who would do it when we were gone and only occasionally).
Interestingly, I actually think it's gotten worse since she's had more variety in food, so I don't see the suggestion of giving her more table scraps in her dish to work. She does get some already (although not much), but that doesn't seem to matter to her. I have been working more on getting her to follow commands in general, though, and I'm hopeful that may help somewhat.
I've never heard of a "scat mat" but will look into it. I think the idea of making it unpleasant to get on the table might be the key. I wouldn't do it because I'd be afraid it might hurt her, but putting a hot chile pepper up there might do the trick...
