Xmingwin is cross-mingwin, that is, mingwin hosted on a "foreign" operating system.
[Explain refs.]
"... grab critcl starkit and cross-compile ..." Use "cross" (critcl).
[Much more to come.]
On Linux side, for example, pick up tclkit [L1 ], then critcl starkit [L2 ] (rename?), then ... http://www.digital-smarties.com/pub/tkspline.tar.gz
http://www.digital-smarties.com/Tcl2002/critcl.pdf has section on cross-compilation with XMingwin.
[Rumor has it standard Win32 binaries for SDL are made with XMingwin.]