You can't stop the negative tapes just by saying you're going to stop thinking these self-critical thoughts -- rather, you have to replace them with something new. A positive tape. She suggests two ways of creating a positive tape; the first one is to sit down with a trusted friend and ask them to spend about 3 minutes talking about precisely what's good about you. Your job is to write it all down (and not argue with your friend!)
I didn't want to do this face-to-face with somebody, so I decided to do a distributed version instead, which I did in this post (and on Facebook, and in one person's case, email). Now that I have some responses, I'm going to try to compile them together into the equivalent of that 3-minute monologue from a friend (combining common themes together).
And then I will have a positive tape (written down, so I can always refresh my memory) that I can always replay when the negative ones are too loud. I don't think my self-esteem is especially low these days, but I still have plenty of self-critical thoughts and some residual impostor syndrome. Also, distinctly from actively thinking bad things about myself, there are plenty of good things about myself that I don't notice on my own.
So, thanks to everyone who commented! I probably won't post the summarized version publicly (too self-absorbed ;) but I appreciate everyone who provided me with raw material for it :) Also, this was a fun experiment and I would wholly recommend it to others.