I think at the moment what we need to do is dial the explanations back into a drip feed, and worry less about "why are we here" and more on "what do we do now".

This might help the tone but at the same time some characters by nature cannot simply settle down and relax. Personally, I can't imagine that the entire cast can realistically stop asking questions and quit digging especially after they were successful uncovering information after diving into Calice and other such activities.

To me the tone of this game greatly resembles the Puella Magi Madoka Magica series. It opens on a friendly lighter-hearted setting but as time goes by it's revealed that there's a practically unbeatable force looming over the scenario with an iron clutch on those who entered.
The best way I can think of to lighten the load of that setup is through humor. Not that Calice is a funny subject but I think that MLP-ifying cross-canon opponents and challenges the way all the offworlders have been pony-fied helps greatly.