Some have had success with older .kext, some have not. Others have tried the Download version rather than the App Store version and still have issues.
If you have a Time Machine backup prior to 11.4, I suggest that is the safest route to take and restore 11.3.x, because it worked for your specific OS X installation.
If Time Machine restore is not an option, instead of trashing just the kext, I suggest throwing away iTunes into Trash, emptying trash, rebooting, and re-installing via the Download route (not the App store route). I suggest verifying the MD5SUMs of the files downloaded. Please make sure that trashing iTunes from Applications does not include anything related to your content. The content location is in iTunes -> Preferences -> Advanced.
Making an extra TM backup, if possible, containing 11.4 will not hurt since it will be an incremental backup.
Of late 10.9.4 (WiFi), MBA EFI (EFI 2.9.x for 2011 models), iTunes 11.4 are updates which Apple could have regression tested better. The marketing push for versions (perhaps to match/support iOS8/Yosemite/iPhone6 are driving such updates, but stability is questionable at best).
The updates are now akin to Java, Windows, Android, etc. 😢