Update:
Ok so I took the needed plunge and uninstalled my keyboard software. Restart. Cleanup of residual folders and files. CCleaner. iTunes still will not release "enable full keyboard integration."
I then uninstalled ALL Apple software. Renamed sentinel file in iTunes folder to sentinel.old and renamed preferences.plist in iTunes Media folder to preferences.plist.old. Restart. Cleanup of residual folders and files. CCleaner. Restart.
Reinstall iTunes with new music library. iTunes still will not release "enable full keyboard integration." Point iTunes to original library. It recreates a new sentinel and preferences.plist but the behavior is of course the same.
I still have not reinstalled they keyboard driver and software that creates this iTunes behavior in the first place.
At this point, I am thinking that the keyboard software must create a new service that continues to run despite the software being uninstalled. This service running must be what clogs up iTunes mini player feature by way of the static ON of the "enable full keyboard integration" setting.
So I begin investigating services. Two catch my attention: "Human Interface Device Service" and, due to what was causing Jeff's issues above, "Touch Keyboard and Handwriting Panel Service." Tried to Stop them both individually and together. Stopping the HID Service prevents my keyboard's media buttons from working. The media keys were working when iTunes was working fine prior to the initial install of keyboard software. Touch Panel Service makes no noticeable effect. Regardless, these services running or not has no bearing on resolving "enable full keyboard integration" to be turned off.
There must be another service running that is causing this that the keyboard software installed, although non jump out at me. I am as stumped as ever, but feel I have made progress nonetheless. At least I will tell myself that!
Uninstalling and reinstalling Apple software is no fun. I do not wish to reinstall my OS again and do need to use the keyboard software for macros and LED controls so even if I clean install yet again, this problem will resurface. There has to be answers and resolution within my existing install. If only I can find it!
That is where I am at this point. Everything back up and running and thank goodness my well groomed iTunes Library in operable order (I always have concerns there also doing stuff like this). I will be leaving the keyboard software uninstalled for now on the manhunt for the mystery service or other cause.