Also attached is an example org file, and the output (in PDF). I do
need a bit of help finishing this off though. I'm not quiet sure how to
get TikZ to do a better job with the layout of the mindmap when you have
several nodes.

I tried the new mindmap function and it looks really nice and run flawless on my system.
I guess for the placement of the nodes there is not much you can do. Personaly I belive that it is at least a very difficulte task, not only to find the required space (which might need some optimisation algorithm) but often mindmaps should be arranged according to the content (e.g. bring similar topics close to each other). I find it already difficult to do it by hand.

Maybe instead of and full automatised version you could try to find a way to define where to place the nodes within org-mode.
Furthermore, I noticed that you define standard colours in styles and override there settings by variables given in the org-file. Since you generate the complete tex-file, might it be possible to define the styles on the fly. This would allow you to remove the color definition in most of the node parameters and make the whole file less verbose.

Since you always create mindmaps you might even reduce

:TIKZ_STYLE: concept color=green
to
:TIKZ_STYLE: green

as for the above described placement, a very easy way to give a rough placement command could be
:TIKZ_STYLE: green, north
with north, northeast, east, etc.
or
:TIKZ_STYLE: green, 90
whereas the number is the degree

Anyone want to help me get this mindmap generator finished?

It is not really a help but at least a feedback

Best regards,

Torsten