I figured out what was wrong with the v3 prototype. It turns out that the case of the SAMS70N19 has two "divots" in the top near two of the corners. One of them is very large, the other one somewhat smaller. Turns out, the big one isn't near pin 1. The smaller one is, along with a chamfered corner. Flipping the chip around the right way allowed it not only to enumerate on the bus, but also to be probed with SWD from my AtmelICE in Atmel Studio.

The only other interesting discovery was that the VBG bias resistor was supposed to be 5.62 kΩ instead of 56 kΩ. Fortunately, that doesn't require changing anything on the board.

The only other thing that's less than perfect about the prototype is that the fine pin pitch of the LQFP package inevitably requires rework after the oven to remove bridging.

So, nothing to do now but get on with the firmware.