How do I cycle through windows without bringing each to the fore?
To continually switch between two windows use Command` and, to go back to the previous window, ShiftCommand`. I tested it with XQuartz and worked as expected.

Otherwise: Can't you select the window you wish to bring to the front from XQuartz's Window menu? 

Other possibility is to use Hot Corners (introduced in OS X 10.3 "Panther") to show all application windows, then choose the one you need. There are plenty of guides out there, for instance http://heresthethingblog.com/2012/02/06/mac-tip-control-desktop-hot-corners/.

Basically (in 10.7 "Lion" and later), you have to open System Preferences, select Mission Control and press the button Hot Corners... in the bottom. Then you can select a corner for action Application Windows.