Is coconut milk and option? You can sub full-fat canned for the yogurt, perhaps cut back a little or add some banana. (Or sweetened condensed coconut milk in the can.)
I make
these with coffee instead of earl gray once or twice every summer. They are decadent. I have made them with canned coconut milk instead of the dairy and they've turned out just fine. There are a couple of brands of sweetened condensed coconut milk on the market (but I can't recall offhand what they are) that are a simple 1:1 substitution. I've seen it at Wegman's, Whole Foods, and a couple of the other larger local chains. I use full-fat coconut milk for most of the rest of the dairy, plus some strong coffee.
(If you've ever seen the recipes for no-churn ice cream, sweetened condensed milk is the secret ingredient in them. It works the same here. I think it's the fat as well as the way the sugar is dissolved in the processing that keeps huge ice crystals from forming so the result is creamy and smooth ice cream without the churning. We've played around with ratios and added in things like pureed fruit, but I don't usually write things down.
)
Another option is to freeze your favorite smoothies.