I can't find this ruling in the Shulchan Aruch, but isn't there a common understanding that an individual shouldn't pray/sing at the very top of their voice in shul (which annoys other congregants and even overpowers the Chazzan)? Can anyone give me an actual Talmudic citation or ruling?
In the laws of Rosh Hashana The Mechaber mentions that even though a whole year one should not daven with a raised voice on Rosh Hashana it is permitted since people are davening from a Machzor and the noise wont disturb them. The source is PisKei Tosfos in Rosh HaShana. Not the Gemorah itself.
That being said the Mishna Brura says that still one should not over do it (yoser m'dai) i.e. daven so loud that it becomes a distraction to others.
If in your Shul people daven in a siddur and not by heart, than it would be permissible to daven loud BUT not so loud that you would disturb other peoples concentration.
This a touchy issue.
First there is this publication by Tzeirei Chasidea Viznitz that speaks strongly against those who want to stop the practice of saying Pesukei Dezimro loud and writes that with the exception of the Amidah, davenning is to be loud and so it sweetens judgement:
וחז"ל העידו בר"ה (דף ט"ז) דצעקה הוא אחד מדברים המבטלין רוע הגזירה, והפייט בפיוט "ותשובה ותפלה וצדקה" הציג צום "קול" ממון, הרי כי תפלה הוא בקול, חוץ מתפלת ח"י ברכות, ועיין' בזוה"ק (פ' שמות דף כ ריש ע"א) גודל שבח הזעקה והצעקה שממתיקין כל הדינים והגזירות
Then O Ch 101(3) speaks about raising the voice in davenning on Rosh Hashono in the Amidah. The MB  on the words of the Rema, “he should not raise his voice too loudly” says:
“because that (raising the voice) comes from the prophets of Baal or because he will surely confuse his neighbour. At all events it seems that those chazzanim who raise their voices to encourage concentration and so that people can clearly hear the words do well. But those who raise their voices to show off their voices do not act properly.”
The various views may perhaps be reconciled to say that raising the voice in prayer to aid concentration is good but it must not disturb others and must not be to show off the voice.
the gemara in brochos says one should not daven so loudly so as not to confuse people that you are the shaliach tzibbur.