I tried mistake-stitch rib (before you suggested it!) and even k1p1 again, but ultimately I decided that brioche was where it was at—thick, plush, dense—and in order to get it tighter, I’d just have to go to smaller needles.
I dropped down to size 3s. In Manos! And it’s created the perfect density. In fact, I bound one of them off just about an hour ago, before leaving for work. I didn’t knit it in the round, because I wasn’t exactly sure that brioche would work in the round. Once I got through some more inches, I knew how I could make it work, but by then I was on a roll and decided that a quick seam down the side wouldn’t be so bad. Plus knitting flat meant I didn’t have to think at all (it’s the same exact row every time; in the round I’d have had to switch each row)—and I hit a particularly pleasant groove with the yo, sl1 combination.
Laura, why did you say that you couldn’t “do it”? If you think brioche would be too hard, just try it! It’s really easy. On an even number of stitchs, the prep row is to yo, sl1, k1. Then all other rows are to yo, sl1, k2tog (knitting together the slipped stitch and the yo). To bind off, I did p1, k2tog across, because otherwise it ended up too tight if I bound off using the slipped stitches without working them. I’m sure this is making sense only to those who’ve worked with brioche before, but in case you try it, that’s the solution I decided on.