Thanks everyone.
Yes, I tried the most recent VirtualBox (as of this morning).
As several of you have suggested, I suspect the issue is specifically around Wi-Fi. In other words, if it were a wired LAN connection, things would have been easier. I mean, having a wired LAN is not out of the question, but would complicated the hardware setup in my case.
I've used USB passthrough with VB many times in the past, but never with a network adapter. Using a PCI card is an interesting suggestion, though the NUC in question only has an M.2 slot (taken by an SSD).