Tilly, I don't have firsthand experience with waiting, but I am under the impression that it's not too late to get some benefits from binding if you start in the first couple of months postpartum.
And an update: I decided to buy a squeem. I got a size L and I'm almost ready to move to a M. Baby is one week old today. As for sizing, I am 5'8" and started this pregnancy at about 145lbs and ended at 173, so almost 30lbs gained. I wore a size 8ish before pregnancy. I had no idea whether if be a M or L for squeem, so I guessed larger. I don't think I could've gotten into a M right away.
A week out, I've been using it everyday, though not all day. I definitely see a difference from how I looked postpartum with my 2 year old. My waist is still thick, and the skin is loose, but I don't have that mom belly, and no one would guess I was pregnant. With DS1 I dropped weight relatively quickly but I had such a big belly that I was still getting guessed pregnant over a month out. So far, I'm pretty pleased with the results and I'm going to continue using it at least another week or two.