That's a pretty big time window - pretty much the same amount of time separates the Columbian Voyage with the invention of the telegraph. Importantly, the time period also includes the first outbreak of the black plague, an event which caused significant disruption to the European financial system and in a way caused a hard reset of sorts - the Financial Industry prior to the mid-14th century exhibited different characteristics compared than industry after the plague subsided.

But there are a few works considered "Classics" in the space which you could pick up and might offer you the background you're looking for:

• The Medici Bank is probably one of the most famous and extensively studied early renaissance financial institutions. You can read all about its rise and fall in The Rise and Decline of the Medici Bank, 1397-1494 by Raymond De Roover. While the work isn't new, it was posthumously revised as late as 1999 (maybe more recently) and given that De Roover was very interested in the mechanics of medieval and renaissance business, his work should offer the level of detail you desire.

• While medieval and early renaissance financial institutions did manage astoundingly long-distance financial networks, the constraints of the time nonetheless meant that the financial industry had very different characteristics in different economic centers. This means that most in-depth studies choose to focus on an individual financial center, rather than attempt a broader analysis. And while the Medici of Florence are Italy's most famous banking dynasty, in the period specified the most vibrant financial center on the peninsula was in fact the city of Venice. Appropriately, you might be interested in an examination of the Venetian financial industry: The Venetian Money Market: Banks, Panics, and the Public Debt, 1200-1500 by Reinhold C. Mueller, who taught for years at Venice's Ca'Foscari University, could interest you in this regard.

• The "Big Bang" moment for contemporary study of the medieval financial system (that is to say, the "starting point" for most contemporary historiographic analysis and generally the groundwork on top of which contemporary studied will build) are the papers presented in the 1977 conference "The dawn of modern banking." This was a few years after the publication of The Tyranny of a Construct, and a hot time to be publishing works which sought to "Reset" analysis of medieval history. If you can get ahold of the collection of papers presented at the conference, published under the same name (The Dawn of Banking, but also sometimes published under the title The Dawn of Modern Banking) the works collected could offer information which will be useful to you.