There are rewards and there are eternal rewards. Is it possible that someone who feeds the hungry will get a reward? Sure. I think it's debatable, but anyone who feeds the hungry might get a reward - but I don't see evidence of an eternal reward. And the promises are (as far as I can tell) in Christ. If you give a prophet a glass of water in Christ's name (that's critical) then you will not fail to receive a prophet's reward. I see that as something that someone not in Christ will not be able to fulfill.
I don't see how the righteous sheep can be righteous outside of Christ (call them the church or whatever you want). If this is possible, then Christ's sacrifice wasn't absolutely essential. I have to disagree here. Unless I'm missing what you are after.
The Jews have national promises. Yes. But when I see that the promise was to Abraham and to his seed (singular), I can't see it any other way than in Christ. Will the Jews be inheritors of glory? Sure...but only in Christ. Will they necessarily be brought there by evangelism as we have understood it? I can't say...possibly not. But that still doesn't mean the promise is outside of Christ.
Can someone conform to what Christ "blessed" in the Beatitudes outside of Him?
Not outside Christ but outside the church....
Yes I believe the church has gotten the great matter of the last judgement wrong since very early on. It's a bold thing to say, I like to think that I am strictly orthodox.
If this present time is made up of just the saved and the damned then a great many things do not make sense in scripture.
Why would we be a city set upon a hill?
Once again if you believe in the Millennial reign [and I do] then your view on the last judgement must change. For we see that the second and last or general resurrection takes place after the church has been raptured, "so shall we ever be with the Lord" and after we have reigned with Him for a thousand years. In view of that there is no way the last judgement which follows the general resurrection can involve the church. Except that He brings us with Him to judge and the world will be judged by us according to Paul.
There are three distinct groups at that judgement. There are the sheep, the goats and then there is that group who the Lord addresses as "these the least of My brethren" that's us, that's the church and Paul's teaching comes into line with it...they [the sheep and the goats] are judged by how they did or did not minister to God's people, thus we will judge the world.