The idea for character movement isn't bad. But if you do have them moving like that, you'll have to place much more detail into all of them, to show little things like maybe their clothes swaying, their hair movement, etc.. But just moving up and down by 1 pixel alone isn't enough to illustrate this effect, in my opinion.
Personally, I think it'd look better without any movement. I like them just standing there, rather than bobbing around (which reminds me of later FF games, where the characters would take up silly stances and jump around in one spot).
I question I have for you is in regards to Rika/Chaz's descendants. Is that going to be avoided, or will someone of their bloodline make an appearance in the game?