Random thoughts too late at night: making a human age like a demon.
Nerd brain should not be awake, but here we are. I think I just figured out a sciencey (if you squint real hard) way to allow for humans to age the same rate as demon partners. In Inuyasha, we know that yoki is the source of Inuyasha's extraordinary healing powers - what if that extended to the DNA? Yoki protects DNA from deteriorating, which is what causes aging. If that is true, it may be possible for a demon to gift their yoki to someone else (a human), which would allow for the human's healing powers to increase and their DNA to not deteriorate as quickly, thus slowing their aging process.
If we assume that a demon’s yoki is a finite resource, giving it to a human would be the equivalent of shaving years off their own lives, so a demon would only do such a thing in a special circumstance. It would also likely need to be something that couldn’t occur just once.
So... if Kagome and Inuyasha are very much in love and happy, once per year on their anniversary, you could imagine Inuyasha gifting Kagome with his yoki - enough to delay her aging process and match up with his. He gives up some of his long life to be with her, and you get an ending that allows the two to be together.
This is not to say that there are not beautiful stories that address how demons would deal with the mortality of human partners, or compelling stories about reincarnation, this is just another way for the “please let our sweet doggie boy live the rest of his life happy with the love of his life” storytellers to write their tales.
No idea how I am going to use my late night nerd brain thoughts yet - maybe I won’t, but I was pleased to find a compelling way to let Kagome and Inuyasha be together, that had some small glimmer of truth (and a little bit science if you squint) to it.