[Rumil]

Interesting thought on 'mumakil',

could it perhaps be Adunaic as used by the Black Numenoreans?

I don't think the hobbit stories of oliphants necessarily mean wooly mammoths on the Tower Hills, though I do sort of like the idea, maybe confined to the far North and hunted by the snowmen of Forochel?

The 'chain' might be another explanation, like for trade goods. For example Bilbo's coffee beans might be grown in Ithilien, traded to Minas Tirith, then Rohan, Isengard, up the Greenway to Bree then to the Shire. Nobody actually travels all the way but the goods get passed along the chain. (An inverse Denethor's umbrella for those that remember the thread!). Likewise stories get passed from person to person and can travel further than the individuals

How about the oliphant description starting in Harad, the men of Khand see the oliphants while serving under Sauron, tell the Easterlings about this impressive beast, who mention it while collecting tribute from the Dorwinrim, who pass the story on the the men of Laketown, who tell the Wood-elves, who compose several poems, lays and theatrical performances on the subject, impressing a visiting elf from Rivendell, who recites his favourite back at home in company with the Rangers, one of whom recounts the amusing story at the Prancing Pony, where it's heard by a visiting Took, who relates this in the Green Dragon, and in five minutes half the Shire has heard of oliphants.

Of course the description might not be terribly accurate by the time it reaches Hobbiton, a bit like Chinese whispers.