Madara said he needed to be revived to become the Juubi's jinchuriki. However, clearly the other jinchuriki revived with edo tensei had their bijuu sealed again. So it is definitely possible to seal a tailed beast in an edo tensei body.
However, who says edo tensei lasts forever? Perhaps there is a time line on it, which ends at some point, which is why Madara needs to be revived to do it, since the eternal genjutsu is pointless, if it ends, when edo tensei ends.
If there is no time dependency on the jutsu, it really makes a huge glitch as well, as it would not explain, the paradox you just mentioned.