I dug through my code and found where I'd fixed it, but it looks like I left no explanation, so I hunted around the net for an explanation and have included the first non-awful one:
https://forums.minecraftforge.net/topic/73175-disable-culling-from-custom-block/

tldr:
I unclude RenderSystem.disableCull(); in the render method of the TileEntity for the custom block. I believe there's also a json variant if you used model files (which I'm too lazy to confirm).