Is there a multi-tab terminal replacement for Cygwin's terminal?
You can use Console to achieve this. Simply configure the Shell under the Settings page to point to Cygwin.bat.
If it is not a problem for you to start sshd and use cygwin via "ssh localhost", try MTPuTTY. It worked great for me.
- full access to PuTTY configurability (and I do not know any better terminal emulator for windows)
- configurable keybindings in MTPuTTY (everything I needed)
mobaxterm might be what you're looking for - basic set of cywin tools (and you can use your own) multi tabs, and an x server baked right in