the problem is that if I choose “Sync Music”, the IPOD then demands that I remove everything on the IPod even though the ipod is synced with the computer.
Um, people, why not select "manually manage" instead of "sync"? I haven't "synced" in years because
a) my music library got bigger than the device capacity
b) issues like @Minsk59 but from sharing a device between multiple computers
As for a different answer to your question, I have not put music in iTunes in ages. I do indeed use it to TRANSFER the music, but via drag-and-drop. In iTunes, you have to get the device (iPod) icon visible, and minimize the iTunes window so you can also see a Finder window. Grab your music file(s) in Finder and drag onto the device icon. Presto! The stuff copies over without actually being in iTunes at all.
Frankly, I've even moved on from this and went to using a Sansa ClipZip and now an AGPTEK MP3 player. Those will play bootleg FLAC files directly as a bonus ;D By the way, if you want to copy/back up those iPod contents, then you pretty much need 3rd party software.