Seed specifically says it does not contain Mooshrooms? I'm not sure if it would be any different when transferred to XBox One. If you haven't already, make a creative version of the seed and fly around mapping / looking for one. That really is the leg work needed if someone doesn't list the coordinates for you. You could also try using chunkbase. I tried quickly out of curiosity and the one coordinate it listed was a not accurate.
Are you already heavily invested in this seed? There are so many seeds for recent XBox One versions that have all structures and all biomes. You might want to consider starting a world in a new one.