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I ultimately came to a conclusion:
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1- If such were the case, failing to wish for the mad love of a fallen angel at the Tanabata would mean that he couldn't possibly have ever shown up in the game at all, as he never would have been freed.
2- Ryouta's familiar with who he is in BBL, recognizing him as a student from the class next door, a member of the manga club, and a reputable nutcase. He couldn't have achieved any of those things in a short amount of time while under literal imprisonment (particularly the reputation, as well as getting registered with the school at all and getting a Student ID).
3- Regardless of whether you choose his route or not prior to BBL engaging, he knows the protagonist and refers to her as Edel Blau. Proven when he identifies her by both names when interrogated by Sakuya and Ryouta.
In short, I'm 100% certain the "Cage of Ice" is not a literal form of imprisonment, merely an embellishment of his head-canon backstory regarding the Crimson Angel's history with the Apostle of the Blue Sky.
Another problem that came up was the nature of his still being a sophomore despite being involved with the medical center studies 5 years ago, during which time he probably would have been a student as well. 2 possible explanations come to mind: St. Pigeonation's is a K-12 type of school, or Anghel's incapable of focusing on his studies well enough to keep from getting held back multiple times. I'm guessing the former, since in the latter case I would think they'd have kicked him out by now.
Anyway, just wanted to get that written down before I forgot.