I did more research; carrageenan is based in Neilson's *chocolate* milk products only. I've tried linking to ingredients of white and chocolate milk, but they have the same website. So, go to Neilson's Dairy website - Products -> Milk (you'll get a listing for all 4 types). Then, on the right-hand side, you can select chocolate milk to see that ingredient list. Yeah. A bit of a difference.
I perused the site some more and found it's in items such as sour cream, but not in (most) yogurts. I found the lower the fat content in yogurt, the more presence of carrageenan. Interesting.
Blue Diamond Almond Milk has a much higher nutritional content than 'regular' milk, but like I said, unfortunately has our friend (as mentioned, 7th ingredient).
For the fun of it, I took a look at another favourite dairy brand, Organic Meadow. Their chocolate milk also has it in it, but no other dairy products do. So there's something about chocolate milk that requires this thickening agent (aside from other products, we agree, but this all started with chocolate milk, so..). As a bonus, their sour cream doesn't contain it, nor their yogurt, though sadly their ice cream does (but it's the very last ingredient).
So, if we're deciding what we're putting into our bodies when it comes to dairy and dairy ingredients, what wins? Choosing one product over another because it has an ingredient we're trying to avoid? Should we always choose organic? Should we look at other options for calcium and vitamin alternatives?