Your explanation for the ending is probably the most satisfactory one and is logical even though the logic is clearly created to justify the happiest possible ending here. Your ending is as justifiable as the one which the writer was initially trying to portray and which got hijacked by the director.
1. Agree. That is the only way it makes sense and is logically implied and necessary for the reaper community as well to maintain some sort of history.
2. Yes, but I see no reason for the timeline to stretch till that point in the past if only Joon was to be removed. Still, that is the only way that new life of hers makes sense. She could not have died and have have been reborn based on Leo's age being similar at the end. Thus, her previous life was just edited to the least extent possible removing Joon. Maybe, saving the parents was a wish grant to 444.
Also addressing the originally proposed ending where Black is just obliterated because:
(i). There was no reason for him not to reveal his reaper personality or his Joon soul to the girl who would probably be the most receptive of all to such a concept, especially since she got her talent from her reaper dad. Hiding this was pure masochism with no benefits. even Ha ram would have been better off knowing the facts.
(ii) There was no attempt at hiding or trying to achieve a solution to living a human self. He simply accepted his fate. I expect more from a hero who displayed resilience throughout.
(iii) If the killing of humans at the end at all was a factor in his fate, it was unnecessary and seemed to be deliberate suicide on his part.
(iv) The rule of Black being unable to return initially because his fate was tied to his partner was incredibly weak. If that is the reason for a major plot device, we can definitely write our happy ending with logic in the most satisfying way without worrying why sadness is more natural.
(v) Finally, the laws of the reaper universe just seem arbitrary. it seems incredibly easy to get on the wrong side of the rules, incredibly easy to fall in love with a human, incredibly easy to change who or when someone is to die, and also incredibly easy to dodge the Death Squad. Based on all this, the enforcement of the dissipation penalty just seems forced. In fact, it seemed that relying on fate or the judgement of God is the worst alternative as the natural sequence of events without 444 would be incredibly unjust.
To me, adding sadness in the drama at the end would be the more contrived alternative, added only for masochistic purposes. The director had differing opinions here and frankly I am gladder he changed it albeit with terrible execution and production values at the end.