The conversation is a little difficult to follow because Jenkins' comments are called "Jenkins Rejoinder" while Hamblin's are called "Jenkins Response" but the numbers assigned don't line up, but it is still worth following if one is interested in these perspectives.
Jenkins makes the argument that Hamblin has no evidence for the Book of Mormon. Here's how he frames it:
As near as I can tell, Hamblin responds with this:
During years of debating the historicity of the Book of Mormon, I’ve found that the real problems have to do with assumptions, presupposition, methodologies, and epistemological questions. Until we can achieve common ground on those issues, debating the specific implications of a particular inscription is pointless. So far, professor Jenkins and I have not arrived at that common ground; far from it. It has been difficult to convince him even that ancient Book of Mormon studies is field of study, and that the evidence should be examined with an open mind. He stubbornly refuses to take seriously either ancient Book of Mormon studies as a field, or the scholars who engage in it. If we can’t arrive at at least a working agreement on that, how can we hope to have a fruitful discussion of the evidentiary significance of Preclassic Mesoamerican pottery?
To me, this is not responsive. I've been reading Sorenson, FARMS, Maxwell Institute, and similar material for decades but so far, like Jenkins, I have not seen a single credible "object or site, one piece of genetic or linguistic evidence" from Mesoamerica that begins to support the historicity of the Book of Mormon.
It's interesting that Jenkins asks, "So why is he not (yet) socking me daily with convincing examples from Oaxaca or Ohio, Michoacán or Michigan?"
The reason: Hamblin has nothing from Oaxaca or Michoacan, and he rejects everything from Ohio and Michigan.
Numerous artifacts have been found in North America that directly support the Book of Mormon, but they are all rejected as "counterfeit" or "frauds" because they don't align with prevailing theories about the origins and culture of the Native American Indians. In some cases, there have been counterfeits, but that raises the question, what were these hucksters copying?
I've looked into some of the claims about these artifacts, and in my view, the question of authenticity of these artifacts needs to be re-examined.
At any rate, Hamblin has no solid response to Jenkins' observation that even BYU has no program for Ancient Book of Mormon Studies (ABMS). Instead, he alludes to BYU professors (including himself) who correlate the Book of Mormon with Mesoamerica--a thought that makes me cringe.
Here are his examples. Note that what he considers ABMS is actually "Book of Mormon in Mesoamerica Studies," excluding North America.