How does one, as an Imam, balance beautifying the recitation with repelling showing off?

Beautifying one's voice when reciting the Quran is desirable and praiseworthy. The forbidden aspect is when the beautification of the voice is intended for showing off (riya') and seeking people's praise. Riya' is countered by achieving sincerity towards Allah, seeking refuge in Him from riya', monitoring one's intention, striving against it, and not paying attention to people's praise.

Al-Ajurri said: "Whoever Allah has blessed with a beautiful voice, let him recite for Allah, not for creation, and let him beware of reciting to be heard in order to gain favor with the listeners."

Ibn Baz said: "Beautifying the voice in recitation is one of the greatest means for contemplation, understanding the meaning, and finding pleasure in listening to the Quran. Any thought of showing off that crosses the Imam's mind is from Satan, so he should not pay attention to it."

Al-Shanqiti said: "If the Imam is keen on being sincere to Allah in his recitation, and on giving the Book of Allah its due in terms of precision, mastery, and safeguarding, and he weeps at its promises and warnings from his heart, not out of showing off or pretense, and he beautifies the Book of Allah and seeks great reward from Allah."