If you have the time and space (and a really good blender) you can totally make your own coconut milk from shredded coconut. Here's a simple recipe that takes about 10 minutes according to the recipe (although with the straining-out I'd plan on 15):
http://wellnessmama.com/2447/homemade-coconut-milk/The stuff in a tin I do keep on hand; I use Native Forest (don't know if you get that there) which has no BPA in the liner. If you can store it at a warmer temp or warm it up before use, then the thick stuff on top isn't so solid - the fats kind of congeal when it's cooler. Shaking the can vigorously before opening it helps too. My kids will happily lick off any of the solid stuff that sticks to the sides if I give them a little spatula. LOL
I know you're concerned about the rice milk - if I remember rightly, the arsenic comes from the rice plant leaching the arsenic from the soil - maybe you could do half-and-half coconut milk and rice milk? Not as thick so more easily drinkable and if you only add even just enough rice milk to thin it to a consistency you like for cooking/drinking/whatever and don't use it often? How old is your LO now? (I lose track!)
Oh, just before I hit Post, I had an inspiration: you could make your own oat milk too. Once you find GF oats, do this:
http://ohsheglows.com/2013/01/10/homemade-oat-milk-easy-fast-cheap/ Definitely soak the oats overnight first - much easier to digest!