So one thing I'm not clear on: is the state of a facedown card as Morph or a Manifest something the controlling player is responsible for visibly tracking? If not, why would you use the marker tokens when you could leave them all blank and hope that your opponent loses track?
A card can be face down for three reasons now:
1) It was cast for 3 colorless mana as a Morph. It is marked as a Morph, and you are responsible for marking it both as a Morph and indicating which Morph it is (i.e., Morph #1, Morph #2, etc). It can be turned up at any time for its Morph cost.
2) It was put onto the battlefield as a Manifest effect. It is marked as a Manifest, and you are responsible for marking it both as a Manifest and indicating which Manifest it is (i.e., Manifest #1, Manifest #2, etc). It can be turned up any time for its mana cost or Morph cost (if it has any).
3) It was turned face-down by some other effect (e.g., Ixidron). It is considered a Morph, and must be identified if its identity is known. So an Ashcloud Phoenix that comes back to the battlefield must always be identified as a Morphed Ashcloud Phoenix. If Ixidron (hopefully not getting reprinted) turns creatures face down, they must all be identified by name as well. It can only be turned up for its Morph cost.