The way I read the OPs post, he has the recoil spring inserted fully while doing this procedure. I am aware of some models where the spring can not be put in after the slide is on. May be one of these? Just not sure of the STI.
But for the OP, If the STI has a normal barrel bushing and spring plug, you should be able to install that after the slide stop is in, thereby the slide will not be under pressure. Makes the whole thing much easier. Just IMHO.