I discovered that there is a limitation to how many Home Screen pages one can have based on iOS & hardware. In my case it was 14 (15 with the app drawer.)
In either case I was unable to arrange my applications inside of folders as they would rubber band or snap back into their original position. I would also have applications disappear if I tried to move them out of a folder onto a Home Screen.
My solution to fixing this was to reorganize apps into folders or delete some applications until free space started showing up on my Home Screens or until I had less than 14 pages of apps. Once I had cleared that up I was able to move applications around in folders properly as well as back onto the Home Screens without issue.
I should also mention that I had so many apps that there was a backlog behind my home Screens such that all my home Screens would fill up until I had either deleted enough apps or placed them into folders to the extent that free space started appearing on my home screens or my last Home Screen page.
Hopefully this helps other folks who might be losing their mind trying to organize their apps in folders!