"The correct term is gyaru"
No, gal is correct. ギャル (gyaru) has only ever been a transliteration of gal.
I think the reason we end up seeing "gyaru" sometimes is that for an english speaker unfamiliar with the specific subculture/archetype, gal would be confusing because it's just a general word for girl. Gyaru draws a clearer distinction by being so obviously foreign as a word.
And damn, we see where Ichiji gets her bust size from, lol. Kinda curious what her dad looks like. Guessing by her brothers, he might be a gyaru-oh looking guy. But it'd be funny if there was a gap there like with Amane's mom and dad, lol. Like if he resembled Otaku-kun in some way. Just like Amane, her taste in men would run in the family.