rxvt gives me what I want. I found this command line somewhere a while ago, and it make rxvt do pretty much what I want:
$ rxvt.exe -sl 1500 -fn "Lucida Console-12" -bg black -fg grey -sr -e bash --login -i
I add a shortcut to
C:\cygwin\bin\rxvt.exe on my Windows desktop, and put that command line as the shortcut's target. Now I'm happy.