So, the big problem with this is that currently Soraka is designed around staying close to her healing target and spamming heals on them rapidly with a very short cooldown. If we switch that to a heal over time effect, then it completely breaks that design apart because of the overlap in the application of the heal over time effect. If we left the heal over time short enough that the effects overlap, then it's such a short duration that there isn't really a point in having it be over time. Functionally, very little changes. If we lengthen the cooldown of her heal, then we make it much easier for her to kite away from enemies and we have to redo all of her numbers (the %max hp cost in particular doesn't really work well with longer CD heals).
On top of that, it has other significant problems in how it goes too far in compromising some of the unique principles of her design. Soraka's unique thing is that she's the only healer good enough to save a life through healing. If she can't do that on someone being focused, what's her function later on in the game? Why have her? What is she doing that everyone else can't do too? Are we going to turn her purely into a sustain machine? That was her gameplay before the rework, and everyone hated it, including the people playing her. On top of that, it's already the role of other healing supports, and just having higher numbers isn't enough to be really special in that department.
I don't think a viable solution to the problem can be found here.