Building a DeWalt Charging Circuit - Getting out of my depth - Help?
Suggestions if I'm heading down the wrong path anywhere above.


I think you are heading down the wrong path. These packs are not designed for charging in series or parallel. In the comments you say that you like their robust casing/materials/and onboard balancing/protection circuit. But for reliable operation you should connect directly to the cells and have a balancing circuit that does all of them at once, so if you do it properly the existing case and balancer are redundant.

I suggest getting a single pack that has the voltage and capacity you require, rather than trying to repurpose a product that was not intended to be used this way.


  Help designing the circuit that can charge these batteries


If you reproduce the charging profile of the DeWalt charger then theoretically it should work. However it may be difficult to get each pack to share the voltage and current equally. Since the cells are deliberately undercharged (presumably to improve shelf life) a bit of imbalance will probably be safe, but there is no guarantee. Are you willing to take the risk?   

If I was using these packs I would make them removable and charge each one separately on the official charger (that's what I do with our drone which takes 6 removable batteries, and it takes half a day to charge 3 sets). This may be unacceptable, in which case you should be looking for another properly engineered solution.