Like you I found that papyrus propagates best by cuttings or by dividing the rhizomes In the spring. That is not to say that it can’t be propagated by seed, but the soil should be keep evenly moist and it may take a month or more to sprout. Many plants do not come true from seed, meaning that the new plant will not be identical to the original plant. A cutting or division means that the same genetic material is used in the new plant so it will be identical.
Since King Tut Papyrus is registered by Proven Winners we are checking further on the legalities of plant propagation and will get back to you soon.