If the President wasn't informed, and Hojo had no use for immortality, then such a project could certainly be thrown out. Why refine it when it isn't personally useful? Any ... 'side effects' surely would be refined over time.

Though Sephiroth himself had been a subject of many experiments, at least he was still human.

... Had been, still human. Now? "I've not seen or heard any .. similar transformations or immortality," he says reluctantly. "Though I avoid the scientists as I am able to these days." Since he was old enough to realize he could simply say no, that they had no control over him no matter what they wanted.. "Nor is it part of anything SOLDIER deals with."

Not yet. Deepground would see to that.