こんにちは (Konnichwa) イ リ ニ and toru e,
Thank you for your question, and good job trying to translate this sentence!
toru e, you're on the right track with how the emphasis changes, but unfortunately もう いっぱい が おなか です (mō ippai ga onaka desu) isn't quite right! Instead you should say もう いっぱい の が おなか です (mō ippai no ga onaka desu).
First let's take a look at the original sentence.
In the sentence もう おなか が いっぱい です (mō onaka ga ippai desu), おなか (onaka) is the subject of the sentence. We know this since it is marked by the identifier particle が (ga).
Now here's the important part: the particle が (ga) marks the subject of a sentence, but the subject has to be a NOUN. In this case, the noun is おなか (onaka) "stomach."
However, if we were to switch this sentence around to say もう いっぱい が おなか です (mō ippai ga onaka desu), the subject becomes いっぱい (ippai), which is an ADJECTIVE. Since we need to use a noun before が (ga), this sentence becomes grammatically incorrect.
Don't worry though! There is an easy fix to make this sentence sound perfectly natural. We can use the particle の (no) to change the adjective いっぱい (ippai) into a noun. To do this, just add の (no) before the particle が (ga):
もう いっぱい の が おなか です (mō ippai no ga onaka desu)
Now that we have a noun before が (ga) this sentence is grammatically correct!
You can read all about how to change adjectives into nouns in this brand new lesson on the particle の (no):
Translation-wise, もう おなか が いっぱい です (mō ippai ga onaka desu) means "(I) am already full," or literally: "(my) stomach is already full."
However, もう いっぱい の が おなか です (mō ippai no ga onaka desu) changes the subject to いっぱい (ippai), so it translates to, "the one that is already full is (my) stomach."
In this sentence, the emphasis is on your "stomach," whereas in the first sentence, the emphasis is on your stomach being "full." Basically, by changing the subject around, it changes what's important in the sentence.
I hope this helped! Please let me know if you have any more questions.
べんきょう を がんばって ください！ (Benkyō o ganbatte kudasai!)