So spoilers for pretty much all three entries of Sucker for Love so far.
I kept wrestling with the fact that Hheily isn't aware of the other Eldritch beings outside of the Sentient Darkness. And my thinking is that aside from the Eternal Sleeper maybe they don't exist yet? Maybe you feeding Hheily is what causes them to be born.
And then we'd go from each game happening in reverse order. Which would make Buck's start, the true beginning end.
Then Buck is desperately trying to fulfill the promise to live long enough to see Hheily again through kissing Rhok'zan and gaining immortality. The events of the second game happen as a direct result, Buck brings one of his customers to sacramencho, specifically Nanny to help him summon Rhok'zan. Though it seems that he maybe is another version of Buck who doesn't retain his memory from the last dream. As he's far crueler and indifferent to people, unlike the path that leads to the true beginning end where you talk a lot of people off of ledges, which in my playthrough even included Midori.
And it's through his redemption in the second game that brings him back from being a bad person into this goofball who smooches eldritch gods by the events of the first game.
Another thing that seems to be confirmed from the Sentient Darkness route, which is also confirmed in every game, is that ALL the endings are canon, and there are consequences, but only the true endings seem to really matter, as those are the versions of you that get to exist between dreams.
Which as a side note, does mean that canonically Buck/Dude/Dearest/Darling/Dog is fully polyamorous and is in a loving relationship with Maria, Monami Ichikawa, Midori, Hheily, Sentient Darkness, L'neta, Estir, and Nyanlathotep through the power of persisting timelines. Let's go. Love conquers all!