I'm not a Jedi, but a ...

[Boo Radley]

OK, instead of "Deity", lets use the term Teacher. Buddha had a system of beliefs, rules, observations that if followed, would lead the believer to a state of enlightenment, or whatever.
There is still interaction and direction.
Not so much with Illuvitar. No burning bushes, no turning himself into a swan for a bit of slap and tickle, no hand writing on the wall.

But, going back to your original question:

...what, if I believed as, say Aragorn or Elrond or Frodo or Galadriel, would be my similar Tolkienesque response?

Chances are your response might be something along the lines of, "I am no member of a religion as I understand the term. Illuvitar created everything and everything is part of Illuvitar. My worship of Him is not required or would even be recognized.
And no, I don't want your magazine."