Apparently, in your thought process, because your recognize that God owns "ALL" the hills and because you recognize that there are far more than "1000" hills with cattle on them on the planet earth, then, it still would be accurate to say that "God does own the cattle on a thousand hills"
If God owns ~ALL~ the hills with cattle on them, then it is true that he owns "cattle on a '1000' hills".
Using the same argument:
Because I recognize that Christ has reigned for "ALL" years since his resurrection, and since I recognize that there have been far more than "1000" years since Jesus' resurrection, then, it still would be accurate to say since the time of Christ's resurrection that "Christ reigned for a thousand years".
If Christ has reigned for all the years since his resurrection, then it is true that Christ reigned for "1000" years.
Interestingly, one of your arguments against amillennialism is that if the millennium is now, then that means that Christ has reigned for more than "1000" years.
You can't have your cake and eat it too.
Jean