Well, we finally have an answer to the age-old "can we special Summon a TOON from the Graveyard sans Toon World provided it was Special Summoned correctly the first time?" question. The answer is a heartfelt NO. Maruno takes the day here. For reference, please see the ruling below, hot off the UD Offical Rulings (soon to be auto-botted) for "Time Machine", stating:
If a Toon Monster like "Toon Mermaid", "Toon Summoned Skull", "Blue-Eyes Toon Dragon", or "Manga Ryu-Ran" is destroyed by battle and set to the Graveyard while "Toon World" is not face-up on the field, "Time Machine" cannot be activated.
Kudos Maruno. Long time coming with that official answer, no?