What am I doing wrong? Do I need to just keep doing steps 1 to 4 and eventually the guitar will hold its tuning? Or is there some other problem?
Floyd Rose style trems are tools that Satan uses to drive innocent, well-intentioned guitar players into raving psychosis.
They're really fun until you need to change strings, then the nightmare starts.
Your first mistake was buying a Floyd Rose equipped guitar. Your second mistake was keeping it. Sell that hellish thing to someone you hate.