I've been looking for a way to do this, and Darrell also mentioned that he was looking for a was to use the Multiple Document Interface with firefox.
I have written a patch that will enable you to only use a single kate window. It is controlled by a kate kconfig option and can be changed under kate's general settings tab.
Looks like the new option is placed in $TDEHOME/share/config/katerc [General] UseInstance=0/1?
I see the check box in your patch, but I haven't yet tried to build.
Something else that might be interesting to add is an override flag that, if passed to Kate, launches in the desired instance mode. For example --sdi or --mdi.
Tim