remote app -- local data

[Frank Cox]

I need to run a program on a computer that I normally access through a tunneled
VNC desktop over SSH. I want to have that remote program save its data on my
local hard drive.

For example, if my remote program was Firefox, I would want anything that I
downloaded to be saved into my local directory, not into a directory on the
remote computer where Firefox is actually running.

Is there a way to achieve this?  On a somewhat related note, is there a way to
tell VNC not to load a full desktop, but but just to run one single program?
ssh -X is too slow over this link.