Well, curiosity got the better of me: I went and got a DEXA scan to determine my body fat percentage. Honestly, I'm really shocked - it's 39%!
We've known for a long time that BMI isn't a great indicator of individual health, and the example we usually hear is about bodybuilders showing up as "obese" on the chart because they carry so much muscular weight. I'm actually the opposite - I show as "normal" on the BMI chart, and am a fairly normal weight/size for my age and height, but I'm quite overweight according to body fat percentage. The technician said this is known as "skinny fat", because I'm not that big, but I have practically no muscle at all. I have big hips and legs and I always assumed there were quads under there, and that my BF% was around 30%. Apparently not!!
This really changes things for me. I've been focusing on weight loss through diet primarily, but obviously I need to start doing some weight training and calisthenics, because it looks like my efforts have just cannibalized my muscle rather than my fat. I also have been eating a mostly vegetarian diet and maybe I haven't been getting enough protein to prevent muscle loss. I'm going to start taking F45 classes for fitness, but I feel really confused about how to proceed in terms of diet now.