I see no inconsistency. In FET, all celestial bodies rotate around the Earth, creating their apparent rising and setting. It would be inconsistent to assume that your comet was the first body not to do that.
I'll agree with you on one point: the rising and setting of the comet works exactly the same way as the other celestial bodies. The comet does slowly move on the celestial sphere, unlike the fixed stars but like the Moon, the Sun and the planets. Over short periods, these celestial bodies can almost be considered as fixed.
But I still have to see a flat Earth model that explains how we see the celestial sphere spinning around the northern and southern celestial poles, the fixed stars forming perfect circles from any point on Earth. Even under EA, something that appears directly overhead is actually directly overhead, which means the fixed stars must travel along latitude lines. A fixed star will always be at zenith at the same latitude, that can be found with the formula 90-d where d is its declination. You can project the position of the stars on a Mercator map to easily see the apparent latitude of the fixed stars :
http://astronomia.blog.br/wp-content/uploads/2013/09/AstronomiaBlogBr-carta-celeste-mercator.pdf . Depending on the flat Earth model, this leads to very strange trajectories and big questions on how we can see the stars the way we can see them.
What we see in the sky is exactly what we expect if we are on a spinning sphere with a fixed celestial sphere around us - or if we were on a fixed sphere with the celestial sphere spinning around us, as we thought for centuries, it doesn't make a difference to the observer. You might say it could be a spinning sphere around a flat Earth, but it doesn't explain how we can see the totality of the celestial sphere at the Equator, only half of it at the poles, and more generally why the angular elevation of the celestial poles and the stars we can or can not see depend only on one thing: latitude.