Was this a new transmission? What you are describing could be an input shaft bearing. If the trans is a used one it very well could be something internal to the trans. Input shaft bearing fits the description you are giving as well as a pilot bearing. The TOB will not make noise after the clutch stops moving with the pedal pressed to the floor because with the pedal all the way down the clutch is disengaged.
2000 Mustang GT Steeda build #48. Bolt ons, suspension, Novi 2000.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.