You should realize that in comparing any two spoken languages, there will almost certainly be sounds that are available in one language, but not in the other, and vice-versa. In addition, there may be sounds that seem to be very similar, but are formed in an entirely different manner between to two languages. So that for someone who's native language is one, what seems to be a close approximation may not seem to be such a close approximation to the speaker of another language.

For instance, I'm a native English speaker and don't think 'Asiana' has any sort of a soft G sound whatsoever. For my way of hearing sounds, the 'She' approximation is the closest I can come. And when 'Asiana' is written in Hangul, it's spelled, '아시아나', with the consonant of the second syllable being a 'shiot' character, which is almost always transliterated as an 'S' or 'Sh', depending on the vowel following it. Typically when the 'ee' vowel follows it as is the case in '아시아나', it is typically transliterate as 'Sh', because to English speakers, that seems to be the overall best approximation.

Anyways, there's certainly no right or wrong answers with this one. Sometimes I can get a bit perturbed by people who try to insist on a certain spelling of a foreign word where they are simply using a transliteration into another alphabet. Sure, there's some really stupid decisions that are made in doing it, so that most foreigners haven't a clue on how to pronounce the word, and just a little common sense by a foreigner could come up with a much better transliteration. But who says that as a native English speaker that all transliterations should cater to me? There's just as valid other transliterations that may be better approximations for other foreigners who aren't native English speakers, but maybe still use the Latin alphabet.

One thing to note, 'Asia' as pronounced by most English speakers that I'm aware of sounds like "Aay zhuh" (two syllables with a long 'a' at the beginning and a 'z' sound for the 's'. Koreans say '아시아', with three syllables, a different 'a' sound, and no 'z'. Koreans do not even have a 'z' sound in their language. So whoever coined the name 'Asiana', most likely just added the 'na' onto 'Asia'. Naturally English speakers want to pronounce it like, 'Asia' with the 'na' added, but need to modify the last 'a' in 'Asia', and make it a stand alone syllable. Koreans don't really modify the '아시아' sound, but just add on the, '나', and maybe reduce the length/slightly modify the second '아'.

I remember years ago when I was trying to learn some basic Korean. One sound I always had trouble with was the 'riul' character when it came inside a word. It's normally transliterated as an 'l' or 'r'. But no matter what variations I could think of for each of those letters, or any where in between, Koreans always told me it didn't sound right. One time I mistakenly pronounced it as a 'd' sound, and suddenly a Korean friend told me I got it right. I ended up learning that for me, it's a cross between a 'd' and an 'l', sort of a rolling 'd', that best allows me to approximate that sound. This doesn't pertain directly to how to pronounce 'Asiana', but really demonstrated to me how many differences there are between people and how they think it's best to approximate sounds and transliterate between languages/alphabets.