New Game+ Possible Bug Question - Minor Spoilers

[Atroth]

I've heard from a friend that apparently there's a bug where, if you start a new game+ at the wrong time, after starting the dragons sub-plot, you lose the opportunity to fight them in the new game plus.

I've recently completed my first play through of the game. I plan to play through at least once more to unlock the second class before seriously starting post game content. However, before I started the new game+, I decided to poke around the first floor of the sixth stratum for a bit. I saved at the submagnetic pole there and then warped back to Armoroad.

Now, before I completed the game I reached the floating island in the sea exploration mode, and got a message telling me to come back later. Once I returned to Armoroad from the sixth stratum, I received the message about the three dragons.

What I want to know is if someone who has experience with new game plus can let me know if it's safe to start a new game plus right now, or if receiving that message after entering the sixth stratum counts as starting the dragon quest line, and I'm in danger of locking myself out of it.

[Kaname]

Never heard of the bug. In the playthrough I just finished, I beat up one dragon, did half of the quest of another and most of the third (lacked antifire and antiwind so I didn't end up doing them), then a NG+, and the dragon quests just restarted themselves, except the one I had already killed. That one respawned normally once I got the moon key back.

[Dangerus]

[Wolkenritter]

[Dangerus]