Momo-chan~~~ ^_^ It's definitely going to the right direction I think~~ I can hear the real tone of your voice a lot clearer than the aishite aishite ato ippun (Which btw, I am sick of hearing now hahaa.) Even though you are using a lot less air here(maybe sometimes you're lacking it even), your notes sound a lot less airy~ XD
I know this is experimental and you took my advice of trying singing completely laid back~ So you prolly notice the lack of breath feeling on your voice XD Which is something to improve on if you do the full version
Having a good breath control will make your voice sounds a lot better
I think the sound of lack of breath in this one is to do with you using too much air on some notes then too little. Whatever sound (loud or soft) you're trying to make, there shouldn't be much difference in the amount of air you blow out. (imagine yourself playing a recorder, you would blow the same amount of air when you play all kinds of notes ^^)
One exercise I think you can try is a non singing one~ You can do while you're watching TV, walking around doing your hair etc XD:
Take a deep breath and make the "fuuuu" sound. Try to do it as long as possible and as sustained as possible. Listen hard to the sound you're making and try to make sure it's not bumpy (i.e. you don't suddenly go a bit louder or softer, make sure it's the same intensity, same volume).
It's actually A LOT harder to do than it sounds lol and you're bound to go a bit bump when you're about to run out of breath~ So give that a try, and when you can do that for a good 10s or so(The longer the merrier), try remember that feeling of the sustained air control and integrate it in your singing~ You'll find the tone of your voice will sound a lot more consistent (I hope) XD
The other thing is the high notes~ like the one at 1:11, Gaki-san's solo~ You pretty much hit it (well, slightly flat if I have to be very picky) But you can hear from the sound that you were kind of VERY conscious with it and a little "omg omg high note" feeling. Try to just go for it, treat it as the same as the notes before it. It might help you to reach it easier with a good sound if you think of the whole line being very high (not just that note), coz that makes you prepare for the middle voice -> head voice conversion, coz that note is in your head voice. Basically that note is not resonating as nicely because something in your body is tensed, most likely to be your throat coz it's a high note and it's natural to try to control and make it hit by tensing up your throat, which ironically doesn't help.
I hope this makes sense and helps you ^^;