The reason that zsh gives the errors reported earlier in this sub-thread will be different to the reason that screen doesn't work.
* https://news.ycombinator.com/item?id=11417227
It's readily apparent from the error messages earlier in this sub-thread that the zsh problem isn't to do with escape sequences. And of course the screen problem (at least the one known so far) is not escape sequences, either.
I haven't tried zsh, but I'm pretty sure you can install it. I installed a bunch of applications, including using third party repos and ppa's. I don't see why zsh would not work.
Perhaps zsh uses some unsupported escape sequences (for instance, screen doesn't seem to work), but you can readily work around that by using another terminal in windows (mintty) or launching a VNC server from Linux and a VNC client to your localhost I assume.