I do indeed discuss this elsewhere! I think the beginning is rather less clear than the end, and I'm not certain it's necessary to pin it to a particular moment. (The Columbian Exchange is more a process than a moment as well, of course.)

The spread of Islam was certainly an extremely important process in the formation of links across medieval Afro-Eurasia, but there are others, and from my perspective the discovery of the cycle of monsoon winds at the end of the first century BCE may be more consequential (although of course using that as the starting point of the Middle Ages would mean that the height of the Roman Empire would be considered 'medieval', and I'm not sure anyone would be willing to accept that). I discuss this in a couple of other pieces on the blog.

To me it makes more sense to orient our periodisations around consequential events and processes than to take terms like 'Middle Ages' and try to find definite start- and endpoints for them. The Columbian Exchange is an era-defining process, and yet it features relatively rarely in the historiography of the Middle Ages. I think that ought to change. Where the beginning of 'pre-Columbian' Middle Ages ought to be placed is, I think, less clear, and (to me) a less interesting question.