So, following up with this:
Changing cables does not solve the problem. It appears the 2016 Macbook Pros may have a design defect: when the USB bus is saturated with high-speed disk I/O, the WiFi may drop out.
The Seagate drive in question is one I've recently turned on encryption for, so it's doing the whole "Encrypting Disk" that takes several days (whole-disk encryption even encrypts free/unused space on the disk). While that encryption is ongoing, there's constant background disk access, and that seems to be what's kicking me off the network.
I have a screaming fast external USB-C SSD that I use for disk clones, and while I'm doing a clone with Carbon Copy Cloner, that can also kick me off the network.
In other words, because the WiFi is connected internally via a USB bridge, saturating the USB bus causes network problems.
For whatever reason, probably dealing with how the bridge is connected, this is much more a problem when I use the left-hand USB ports than when I use the right-hand USB ports on the MBP.
