Have you thought of self insert's canon endings out of the eight presented in Perfect Love based on which options he's most likely to choose? And also, I don't know if you've talked about this before, but what nickname would he give Milo?
With his type of character, I feel like he would have his own separate ending due to some differences between him and Eris... naturally. The nuance can be minimal but important enough to result in something different by the end. But to answer the question specifically...
In terms of choosing within the canon endings, above all else, the "Husband" ending is the most likely.
Avoidant of others, the batting cages would be the better option to them. And as someone who was just like Milo before, he'd know just the kind of frustration one can build up in that position, so it's beneficial. From there, stalking Ryan would be chosen out of familiarity and already knowing some information beforehand. Might as well put it to use, direct drugging might be too obvious...
Finally, "protect me" is the closest and most ideal final option. He's always liked to stay in his cage.
He would be off-put by having nicknames right away. That would be put in place when there's enough sufficient change in behavior after whatever the first choice is, as it suggests time has passed. The nicknames would be determined by which route was taken by then.
With the game's specific paths, though, he would attempt to make Milo choose the nicknames instead if insisted. But if it really comes down to his own choice...
In general, the default nickname above all else would be "my lustrous" or more normally "my beloved / love."
With Manipulation route, in the height of things, it would be...
Milo -> Lee: "my god"
Lee -> Milo: "my pet", maybe "my servant" in specific situations.
I imagine Lee would have a habit to include various flairs of endearment like "dear" and "lovely" and the such in addition to the nickname, mainly to emphasize. (e.g. "my dear servant")
With Violence route, in the height of things, it would be...
Milo -> Lee: "my pet"
Lee -> Milo: "my god", maybe "my savior" in specific situations.
I imagine Milo might have more that allude to how weak or fragile Lee is, at some point. But those are less definitive as nicknames, so I won't list them here.
Towards the end of each route, "my prey" could also be used. (Manipulation Lee -> Milo / Violence Milo -> Lee, specifically)
In terms of the endings, at the fullest of becoming each other's perfect love, "my everything" would be used unexceptionally.
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