My answer is really from a different perspective entirely:
d) Middle-earth* changed over time in Tolkien's conception. Giants were ok when he wrote _The Hobbit_ but as he expanded and reconsidered the entire history during the writing of _The Lord of the Rings_ they seem to have dropped out of existence. Sort of. On Caradhras, they were apparently mostly-metaphorical, not physically real. Maybe. In _The Hobbit_ they were probably real (but your speculation about Bilbo exaggerating has some merit as well). Things changed.
So the answer is exactly what you'd expect from an Elvish history, "both no and yes", just like all Elvish advice. <g>
Aside: I, for one, am thankful that Tolkien never got very far with his late-in-life complete rewriting of the legends, with, for example, the world having always been a round ball from the beginning. I think the rounding of the Earth at the fall of Numenor is one of the coolest things in the whole legendarium, and I have no problem at all with Illuvatar making such a retroactive change to Arda, so that
a) it used to be flat, but
b) now it is round and has always been round, but a) is still true.
That's just the sort of thing that only a transcendent deity could accomplish, exactly because to us it is incomprehensible.
Of course, Tolkien, as a good Augustinian, would no doubt disagree: he would not allow even Illuvatar to transcend Logic.
* not "Middle Earth" - this is one of those hyphenated "this was a single word in Westron" things, I believe.