aaaaand never mind. Finally solved it.
In case anyone else runs into this, I just had to add an “!important” to what I was trying to target:
.home .entry-hero {
z-index:0;
}
did not do the trick, but
.home .entry-hero {
z-index:0 !important;
}
did.
Not sure if this is the “correct” way to do it – I hear using “!important” too much can sometimes send you down a haphazard rabbit-hole of coding mistakes, but it seems to work for this.