How do I get purchased and ripped music from my iPhone to iTunes when it won't sync the traditional ways
This can definitely be done, one of two ways.

Free way and non-free way

FREE WAY


Download MediaMonkey, free version
Install and in preferences or settings modify (if needed) where you want things to be sync'd (from phone to pc).
Plug your phone in, sync.  It's not made by Apple so it'll pull every song off your phone and onto your harddrive
May need to move songs from the MediaMonkey location to iTunes location
May need to deal with some dupes


NON-FREE WAY


Read this article how-to-copy-music-from-your-iphone-ipad-or-ipod-touch-to-your-computer-for-free
Buy referenced software and follow their instrux.  Likely very similar to above steps


If you're going the buy route, check out this company as they make good stuff Macroplant iExplorer

Finally if you're on a Mac you'll need to substitute Doubletwist for MediaMonkey