I'm away from my home Linux machine now, but this sounds like maybe

Geany doesn't call
http://developer.gnome.org/gtk3/stable/GtkWindow.html#gtk-window-set-transient-for
for the Search dialog. That's at least the first thing to investigate.
This is a function call though, not an option you can tweak without
code changes. Perhaps someone developer who actually runs multi-head
knows more ...