8.25 for dummie (me)

Your correct that if you tightened it too much the pinion bearing preload would be too much. Is this slop side to side or rotating slop? If it's rotating slop that's possibly just backlash your feeling. If it's side to side slop it's probably bad pinion bearings. The hum is also indicative of bad bearings. I always replace the crush sleeve with a crush sleeve eliminator kit. Makes the setup easier and eliminates the chance of the crush sleeve collapsing.