I understand that Joseph Smith attributed his revelation to a prophet of Jesus named "Mormon" a 4th century indigenous Native American whose name was, apparently according to Smith himself, a contraction of the modern English word "More," and the Egyptian word "Mon," (supposedly meaning good).
Did "More" as an English word exist in the mid-4th century? Does "Mon" mean good in Egyptian?
Was Joseph Smith familiar with Egyptian? Is there any account of how he came up with that or why he chose it, beyond his above referenced account?
Did people raise any objections to the, what seems to be obviously ridiculous, claim that 4 century Native Americans named their kids by combining modern English and Ancient Egyptian?
First of all, let's look at what the LDS church has to say about this etymology from Joseph Smith. Paul Y. Hoskisson wrote two articles critiquing the etymology attributed to Smith and offering other theories. It is interesting to note that the current LDS church has a uniformly negative view of this etymology, even though it is attributed to their prophet in an LDS newspaper. Hoskisson's first article offers several reasons why it should be ignored: (1) that it's "satirical" in response to libelous etymologies of Mormon published by critics; (2) other evidence suggests that the etymology was concocted by W. W. Phelps and perhaps submitted to Smith for approval; (3) an LDS official church historian considered that the etymology was completely the work of Phelps and so it should not be attributed to Smith at all, even though the LDS newspaper attributed it to Smith. An LDS apostle has also more directly stated that the etymology given by Smith appears wrong, telling believers that he "the words more good are not a cognate of the word Mormon" but going on to explain that it would be nice if we took the false etymology as a moral guideline.
We can therefore see that Mormons are in search of a superior etymology, and in part 2 of his article Hoskisson summarizes several suggestions derived from actual ancient Egyptian inscriptions reading mrmnu, mr-mn, or mr. I don't want to pad out this answer by describing these exuberant suggestions in full, so if you are curious, you can click the link. Joseph Smith would not have had access to these Egyptological transcriptions, and he never gave any explanation other than "mon" which, as you anticipated, is not really an Egyptian word. (LDS does not claim that ancient Americans spoke modern English, so the "mor" part is even more inexplicable to them.)
So then, what is the "actual" etymology of Mormon? The scholarly opinion is certainly not that it derives from Egyptian or ancient American terminology. LDS claims about their scripture's basis in real Mesoamerican history have been uniformly rejected by outsiders. I don't think any outsider has written about the "more good" claim but I don't think it would be taken seriously either, as it seems invented on the spur of the moment.
Most historians who write about Mormonism do not care to run through Joseph Smith's geography and names with a fine-tooth comb, because there's limited objective information about his sources of inspiration, and limited practical benefit to critiquing LDS self-identity on linguistic grounds. For instance, there are LDS critics who claim that Mormon's son Moroni got his name from a little-known city in the Indian Ocean, but they are not academic scholars. An important aspect of this for academic religious scholarship is that we have no evidence from anyone close to Joseph Smith that he considered himself a fabulist or that he was excited by other stories besides the Bible, the related journey of the Israelites through Egypt, and his own discoveries revealed in the Book of Mormon and other "translations". That may sound silly, but there have been religious leaders, such as L. Ron Hubbard, who made reading and writing fiction a major part of their careers, and objective scholarship values such statements highly.
Various sources have been proposed for the Book of Mormon. Myths of Israelites coming to North America were published in several books in Joseph Smith's time, and several historians have commented on the 1823 book View of the Hebrews in particular. Joseph Smith did not directly plagiarize any of these books and in fact it's not totally clear that he was familiar with them. More obviously, the Book of Mormon closely imitates the language of the King James Bible and the many Semitic names that appear in it such as Moloch, Solomon, and Moriah. This is really the closest we can get to any sort of secular origin for "Mormon".