I had a few hours in the car yesterday to ponder things (in the mountains this weekend...beautiful) and I think there's one aspect here that's being miscommunicated or misunderstood. I honestly don't think it's important in a discussion about mechanics, because it's about interpretation and theme, and that's entirely subjective. But I do think it's interesting, and maybe others agree.
First of all, I have not been arguing that spending Hope represents "invoking the power of Eru", which sounds to me like a high level D&D cleric casting a spell. But neither is it mundane "inner strength" or determination or "the power of positive thinking".
The analogue that occurs to me is faith/prayer among many real world people with strong religious belief. I can imagine the following conversation:
"I've been unemployed for a long time, and have been tempted to just (insert low-paying temporary work), but God had a plan for me and I prayed and trusted in God, which helped me overcome my self-doubt and fear. And when I got there, when I overcame those fears, I felt closer to God. And that's when this perfect job appeared! Isn't it miraculous!"
And the atheist friend replies, "Well, I guess that's the power of positive thinking. Finding that job had nothing to do with your faith, but...sure...without your faith you might have given up earlier."
Was the appearance of the job actually tied to Faith, or was the friend right that the faith just gave the person confidence to keep looking? In other words, is the Faith delusional?
I don't know. The answer to that question is above my pay grade. But I do know that if I were writing, or playing, an RPG that is basically about that person's religion, I would expect the Faith mechanic to be more than just delusional self-confidence. It would be tied to the mystical/magical/divine/whatever powers that lie beyond the veil in that world.
Given not only the themes that reappear throughout Tolkien's writing, not to mention his real life religious faith, my interpretation is that Hope is a similar thing. Basically the same thing as Faith, but a better word choice for Tolkien's setting. When Sam stabbed Shelob, it wasn't just his determination, and it wasn't just lucky bodily kinesthetics/physics. But neither was it Sam saying, "Eru, save me!" and being visited by a supernatural being. It was something in between; something more subtle. Sam's goodness, and his love for Frodo, and the value he places on gardens over gold, resulted in him doing something that a selfish, petty person would not have been able to do. Because that's how things work in Arda.
Now, I think the books are infused with evidence that this is all thematically appropriate. You may feel differently. I don't want to argue about how to interpret Tolkien. And I certainly don't think that my interpretation points definitively to a specific Hope mechanic. (I mean, obviously I think it points more toward the 1e version, but that's just my opinion.).
But it's been bugging me that what I've been saying gets interpreted as "intervention by Eru" or whatever.