Are you sure about that late 19th c American Ricardian? I only know of one in that time period, Henry Cabot Lodge, and I don't think he did it. I think the 19 c Ricardian in question was an antiquarian, and one of your own.
Michael Bennett, The Battle of Bosworth, says the cairn was erected in 1813. That puts it closer to the time of the reprint of Hutton's Battle of Bosworth. In fact, J. N. Nichols, in his preface to the 1813 reprint, quotes one S. Parr as saying "...It was in dirty, mossy ground, and seemed to me in dange of being destroyed by the cattle. I therefore bestirred myself to have it preserved....... Now Lord Wentworth, and some other Gentlemen, mean to fence the place with some strong stones, and to put a large stone over it with the following inscription; and you may tell the story if you please. Yours, &c. S. Parr
The current inscription suggests that the bit about the American Ricardians may be correct, but at a somewhat later date and as a restoration of the original. Here is a translation:
"Richard III, King of England, slaked his thirst with water drawn from this well when engaged in most bitter and furious battle with Henry, Earl of Richmond, and before being deprived of both his life and his sceptre on the morning of 22nd August A.D. 1485. Those who came afterwards have re-built this structure, damaged as it was by the passage of time. A.D. 1964"
I have some friends who recall shimmying under fences and clambering through weeds to see the cairn in the late 1960s and mid-1970s. How times change...
For more information, including a link to the Battlefield Centre site, seehttp://www.r3.org/bosworth/