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.
other examples
星の形に石を置く。(=石を星の形に置く。)
The shape made by stones is a star shape.
星の形をした石を置く。(=星の形の石を置く。)
The shape of the stone(s) is a star shape.
輪の形に人が並ぶ。(=人が輪の形に並ぶ。)
輪の形をした人が並ぶ。(=輪の形の人が並ぶ。)
In the latter sentences, "the person/people whose shape is a ring" doesn't make much sense.
Yの形に道が分かれる。(=道がYの形に分かれる。)
Yの形をした道が分かれる。(=Yの形の道が分かれる。)
The latter ones don't make much sense, either.
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