It's not really a write up but:
Flash the ESP8266 with JeeLabs esp-link,
https://github.com/jeelabs/esp-link, and configure it for your network. Finally, set the IP and Port in weewx.conf, and that's all she wrote!
Obviously, you need good wifi signal, and this comes with all the downsides of most other homebrew connections, no local storage, so if Weewx stops running, that data is lost, requires software archiving, etc. But it comes with the benefit of no unsightly cables. It will also only work with the consoles that were released before they started baking in the DRM, (green dot consoles as they have been referred to) I'm sure that both of these can be addressed with the rest of the work that DeKay has done, but I haven't taken the time to do so for my module.
The OP's solution is even easier, although more expensive, but also much more robust. Take the Vantage Serial module from Davis, plug it into a Serial Server:
https://www.ebay.com/i/292322627039?rt=nc, plug in a network cable, and get it on the network, again configuring Weewx for IP, with the correct address and port. This *shouldn't* have any of the same limitations that my solution does. Since you are using the 'proper' module, DRM isn't an issue, and the storage is there, ready to be accessed.
A third option is to purchase Davis's Weatherlink IP:
https://www.davisnet.com/product/weatherlinkip-for-vantage-stations/ which does the same as the OP's solution, without any adational hardware. Depending on your needs and pocket book, this may be the 'best' solution, as there are less peices to fail, and Davis has presumably spent many hours and $$ engeniering the solution.
PS. Sorry for the hijack!