If we look at an online dictionary: https://kotobank.jp/word/%E4%B8%80%E6%9D%AF-434512
We can notice one thing, when いっぱい is used without a particle, it is used as a noun.
５ 名詞の下に付き、接尾語的に用いて、限度ぎりぎりまで、の意を表す。「精一杯働く」「時間一杯考える」「腹一杯食べる」 > This one
So in combination with another noun, it forms what we can translate as an adverb/expression.
It basically means "until the limits", so we could understand the first sentence as:
日光は運動場いっぱいでした。: sunlight was playground-full
It doesn't make much sense said this way, but basically, what is being described in the sentence is 日光, and what we say about it is that it was いっぱい until the limits of the 運動場.
Whereas your sentence B:
Describes 日光, but what was いっぱい is not the 日光, but rather the 運動場, so the particle が completely changes the meaning of the sentence, and it doesn't make much sense anymore. (at least to me)
Note that we could maybe turn this sentence into something by assuming that 日光 is the name of a city, and not the word for "sunlight".
As for your third sentence:
運動場は日光でいっぱいでした。: The stadium was full of light
It is correct, but as you can see it doesn't really mean the same thing as the two other sentences. Here what is being described is the 運動場 and not the 日光 itself.