This actually works really well. I'm impressed.
I did spend a little time fucking around with Xming, which has the really annoying behaviour of randomly not starting a font server properly sometimes. I'm now using VcXsrv instead, which is working flawlessly. I wrote a batch script to start everything up on login, and now I can't believe it's not Linux!
There are a couple of caveats, though.
First, I tried upgrading from Ubuntu 14.04 to the latest Debian. The upgrade worked, but the Linux emulation in Windows doesn't support all the features expected by a newer distribution, so some things just don't work right. I've reinstalled on Ubuntu 14.04 now, with the
i3 package repo and
this backports PPA so I get modern versions of i3 and HexChat, and that seems to work ok.
Second, some programs simply don't work. Iridium is one (and probably also Chromium/Chrome, though I haven't tested those), because the Linux sandboxing mechanism isn't implemented. i3status from the i3 package repo segfaults, but the (older) version from the Ubuntu repo works fine.
Third, I had to do some messing around to get i3 set up the way I like it, since by default the Windows key is intercepted by Windows and brings up the Start menu. By carefully remapping things around a bit in Windows, I now have that functioning as a meta key in i3, with F12 bringing up the Start menu if I need it.
All things considered, I can now use my Windows system as though it were Linux, with very few signs that it's not. The main thing I'm still a little irked about is not being able to use Iridium, as I much prefer that to Firefox, but any browser will browse.