I have been working on the exercises(sirens and transcending), not mastered but getting them, and I am at a loss of how they are to be applied in an actual performance context. I am definitely improving at the exercises themselves, but feel sort of like " I can do this new 3 leaf clover tongue trick(random example), is there anything can I do with it?" When I start to strain in the higher notes when I am learning a new song, am I to "transcend" backwards slightly up towards head voice and then eventually that sound produced there gets better with the exercise practice? I listen mainly to bands like the strokes and KOL and am suspicious I don't have a major need for much head voice (not singing Maroon 5.) I might be missing the point here. I enjoy the book! Just trying to figure out how to apply it! Any insight would be most appreciated! - Mike

Exercises so far.
https://soundcloud.com/mikeylikesit182/sirenstransloud11-7-14

These teach us that force is not always necessary to achieve volume and texture, they are also quite literally an exercise for the chord to build strength. The Sirens work with bridging the different resonant chambers (aka - head voice to chest voice) whereas the transcending tones - if done properly help with volume strength.

From the audio you provided you are doing the TT properly - I wouldn't hold the falsetto for as long as you did - but still, you begin in falsetto and bring the chords together while increasing "push" and volume. You also want to make sure with the TT's that your starting pitch and ending pitch are the same.
Your sirens however are incorrect - you are starting right, but ending in Falsetto - keep it in full voice, or "fully connected tone" otherwise you're missing the whole point if the exercise. Be soft volume wise if you have to, but keep the chords connected, it should not be breathy. Also work on mastering one direction before compounding the exercises, otherwise you'll have to break bad habits/relearn with all of them. If Octave Sirens are too difficult then work up in 3rds or 5ths until you are comfortable; Then work up to the octaves and double octave sirens.

Any vocal exercise is meant to build a strong foundation to your singing. They breakdown the different steps in actual singing to focus on certain aspects like developing support, tone, placement, range, projection, etc… When we sing a song, everything is happening at the same time and we loose control. That is why it is preferable to work on things seperately and slowly increase the difficulty levels. You may not want to use your head voice now but if I were you I would still work on developing it for future purposes.