Those two expressions are similar in meaning as a result in your example sentence, but those are different. に indicates result of action/change, so it expresses that the floor extends in a semi-elliptic shape. On the other hand, in 半楕円の形をした床が広がる, 半楕円の形をした modifies 床, so it means "the semi-elliptic floor extends" (i.e., the shape of the floor is semi‐ellipsoid). Thus, ～の形をした is more likely close to ～の形の, not ～の形に.
半楕円の形に and 床が are two independent (not in modifying relation) phrases in the original sentence, so another word order 床が半楕円の形に広がる is also possible without changing the meaning, but 床が半楕円の形をした広がる and 床が半楕円の形の広がる are both ungrammatical.
The shape made by stones is a star shape.
The shape of the stone(s) is a star shape.
In the latter sentences, "the person/people whose shape is a ring" doesn't make much sense.
The latter ones don't make much sense, either.