Need creative help

I have an interesting machining problem that I need help with. I
have to "profile bore" a toroidal shape inside of a cylinder. Surface
finish and accuracy are important. (surface finish 16 micro inch Ra or
better, profile within .001")
Traditional boring probably won't work because the constraints force
the bar to be small (3/4") with a large overhang (1 inch). Chatter and
deflection very likely. The entrance bore is 48mm and the tool must
plunge 28mm to max depth.
I am planning on using a large diameter bar that will go completely
through the part and engage into a pilot bushing into the headstock.
Then the cutting tool will trace a sphere inside the part. The part
will be hogged out separately, so I will only have to remove .020" or
less with the special tool.
I would like to know if anyone can point me to some specialized
boring equipment that could perform this task, or offer some ideas on
how I could make my own tool to do the job. I don't care if it uses CNC
or some other technique (cam follower, tracer, etc.). I am prepared to
do either one.
I can email a section view of the bore if anyone thinks they can
offer advice. All help is appreciated.
Thanks