Yes, I do.
- Connect your phone to your computer and click on the device icon that will appear at the top of the iTunes window:

- this will display the Device/Settings/Summary pane
- using the screenshot below as your guide, switch to the Device/Settings/Music pane (1.):

- make sure that Sync Music (2.) is selected (i.e. that there is a tick in the box)
- for the next option, choose the Entire music library option (3.) to which you have referred. Note that sections numbered 4. will not be shown if you choose this option
- tap the Apply (or Sync) button in the lower right corner of the iTunes window (not shown in the screenshots)
This should add all your music to your iPhone. If it doesn't, post back and we can sort it out. There are other options that may have been changed, which can affect what is added to the phone. Examples include:
- incompatible format for the music (unlikely)
- some or many of your songs are not ticked (and the option to sync only ticked songs and videos is still turned on (it may read "sync only checked songs and videos" if you use the US format). If you come across that option and find it is on, I recommend that you do not turn it off
- something wrong with the song file (such as file missing or faulty file/download). You can check, does a missing song play in your iTunes Library? If not, that's what we investigate
If there is something more to "all music is skewed severely" than it doesn't copy onto your phone? If so, please provide more detail, because although I would (and do) use the word skewed, my use of it may not be the same as yours.