Arigatou. However, these aren't the forms I'm looking for as they don't directly modify the way or quality of the singing itself.
The romanization of the Japanese syllable was made to help people learn Japanese. It's used to represent the sound of a Japanese syllable using roman letters. It's not a conversion of the Japanese syllable to the English syllable. There are many systems used. The common ones are Hepurn - used in a lot of signs, older textbooks and shows. And Kunrei Shiki, used commonly in newer Japanese learning books, and also the one you used above.

In English, we may have [sa si su se so], {sha shi shu she sho} and (sya syi syu sye syo). There are far more distinct sounds in English than in Japanese.

In Japanese, there is さ し す せ そ which are pronounced sa shi su se so. Even though it resembles the order of the English syllable, it's doesn't. し is pronounced shi and not si. There is no si sound in Japanese.

So even though や ゆ よ are pronounced ya yu yo respectively, it doesn't mean they they turn しゅ into syu. It's just the way the Japanese write the sound sha. Don't pronounce it as a combination of two syllables, pronounce it as a whole new syllable on it's own.

Some sound have very subtle differences which we may not be accustomed to hear. Consider す ず つ they are represented as su zu and tsu. The su and zu sound quite like how we say it in English. However the tsu actually has a slight tongue flick from the tip of your upper front teeth then down. it's subtle, but very noticeable to the Japanese.

Another problem is ら り る れ ろ they are often romanized as  ra ri ru re ro. But if you watch dramas or hear real Japanese speak. it will come out either as la li lu le lo or ra ri ru re ro or a mixture. Actually, to the Japanese it's very hard to tell the difference between the r and l sound. Depending to out exposure to language when we're growing up, the brain develops different degrees of sound separation. Each language is unique. English speakers are can differentiate r and l very easily, and we Malaysian who speak many languages can difference very very small differences. When you hear the Japanese rock singers rolling their r, the Japanese do hear the r too, but at a very much lesser degree. To them, it's not much different from lolling the l.

Beware of が ぎ ぐ げ ご , alot of us say them as gar gi gur gey gour. The mistake here it to have the trailing r at the end of ga gu and go and the trailing y at the end of ge. Not only does it sound weird, it also lengthens the duration you are saying the syllable. The duration of each syllable must be very uniform is Japanese. Any stress on a syllable conveys a a certain emotion or expression, and with culture, there are certain words which are stress and not. Also ga sounds closer to nga than gar. gi gu ge go just sound slightly different from ki ku ke ko, don't emphasize the g too much.

The best way is to listen to phonetic lessons offered by native Japanese. There are also on the web. You can see and pick up the correct sound better when it's spoken slowly and articulated well. The actors in dramas talk way to fast.

Hope this helps and have fun learning Japanese.