I have the white mushroom right now and it was made in the overworld. The only thing the other mushroom spores need is a really dark area and need to be on mycelium. Once I got both brown and red mushroom spores I still kept the area dark and was able to breed it into the white mushrooms. It took a lot of time but it worked, didn't need to go in the nether once.
There also cannot be any blocks directly on top of the crops, or else the tooltip will say the plant cannot grow.
Also, can you still craft the super builder's wand? Sorry if this was mentioned somewhere else, but the recipe seemed to be different from the normal extra utilities one, if there is one.