Inulin is slightly tricky to work with because it clumps up easily when it comes into contact with liquid (likely for the same reason, when baking with it I prefer ghee to butter), but it mixes into the heated custard base on the stove without too much trouble as long as you stir well while pouring it in.
Another tip that's worked well for me: instead of milk or half-and-half, I use a 50:50 ratio of heavy cream to egg white + coconut water. In other words, I use whole eggs and then add an amount of coconut water that matches the difference between volumes of heavy cream and egg white. I don't recall offhand how the math on that works out (it's somewhere in an old ChatGPT log that I've been meaning to properly document), but it's a lot easier than separating yolks and it gets a great result with less sugar than milk or half-and-half.
1: https://www.lowcarbfoods.com/low-carb-white-sugar-sweetener-...
Maybe there are other substitute sugars out there which work well at low temperatures?