In case anyone's looking at this in future:

I installed npcap 1.60 (from the .exe installer, all releases available here).

Downloaded the win32 binary for nmrpflash from here and the '-factory' image for WNDR3700v4 from the repo here.

I set a static IP for the ethernet interface on the laptop (after flashing, the router will come up in 192.168.1.1, so 192.168.1.101 makes life slightly simpler), and followed the (simple) instructions for nmrpflash:

NOTE: Check these instructions yourself at the nmrpflash GitHub page. (I'm not responsible for something going wrong.)

i) Start with the router powered off.
ii) Execute with -L to find the target interface.
iii) Execute the flash command, when you see 'Waiting for Ethernet', power on the router.
iv) Following badulesia's advice - wait some extra time after 'Reboot your device' message (I gave it three minutes) before power cycling.
v) Give the router a few minutes to boot. Relax.
vi) Login (root, no pass) at 192.168.1.1.
vii) Do a little dance.

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