Okay, so, a little update. I've switched to (sometimes diluted, sometimes not) baking soda for soap and shampoo and (diluted) vinegar for conditioner. I also pour the diluted vinegar over my skin--I figure it could use conditioning too, since it feels a bit dry after the baking soda.
I've also stopped using toothpaste--now it's just a wet toothbrush with a drop of peppermint extract since I'm so used to tasting mint when brushing my teeth. I'm thinking of doing peroxide and baking soda once per week or so, but the first time I ended up spitting blood, so maybe not a good idea? But other than that, it seems to work just as well as using toothpaste--my teeth feel smooth and clean all day and without that thick toothpaste flavor.
As for the shower ... so far, I feel about the same when getting out as I did when using soap, shampoo, and conditioner, and my hair has felt pretty clean and was no less managable than before, so that's mostly a win as well. Except that today, my hair seems oily and bleh. Did I maybe not use enough baking soda and vinegar last night, or is it my hair adjusting to the change? I've heard people say that it takes a week to adjust, but I figured if that was the case, this would have started sooner. I used the baking soda/vinegar combo for the first time on Friday, and it's now Monday--I shower once a day, in the evening.
Someone recommended aloe as shaving gel, since I don't want oil gunking up the razor. I have not been able to find aloe locally yet, so I tried using some stuff I have that's for treating sunburns that I think is mostly aloe, but with stuff like rubbing alchohol added. That worked pretty well, so I think the aloe idea might be a win too.