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It isn't Cave of Trials but Festia in general that 'bamboozled' you; all attractions and mini-games are on maintenance during those hours (the Festia wiki page has this information). It would've indeed been nice if this were specifically mentioned though.
I don't remember if this was even made clear in the introduction quest to Festia but when talking to Fez and Tia (and other staff) now, only Tia mentions those hours, but in a confusing/misinformative way:
If your mini-game or attraction ends abnormally, or if you forfeit and leave the game, the results won't be reflected in your rank. The same rule applies when games end on a Wednesday between midnight and 7:00 AM. Avoid those times if you're looking to rank high. Don't worry, though! You'll still be able to receive a reward box!
If you change channel right after you sweep you don't even have to wait the 60 seconds of summon cooldown. It'll take less than a minute per Trunk that way, plus you conserve summon time. The method's rather annoying though.
The titles from the reward box give stats (but no visual effects); you can find them on the wiki (assuming they're the same as the previous version of this event).
The 50 win, 30 2nd and 10 lose titles have visual effects but no stats; the one from 70 wins gives +15 max damage, +10% crit and +3% movement speed. Not too bad but good luck getting that with only 90 tries.
You can have multiple boxes but you can only have one Empty Blue Prism at a time. Once that prism is full (and converted) you can open the next box, even if you haven't used the full prism yet. Also, you can stack the filled Blue Prisms
To answer my own question from earlier: there is no expiration timer on the Blue Prism, so you can save it for whenever you need it.