Transmitting rotational motion along shaft

Hi all. I have a mechanical design puzzle which I hope the collective
wisdom here can help me with. In an apparatus I'm building, I have a
block on a leadscrew driven by a motor. On the block is mounted a
mechanism with another leadscrew which needs to be driven at a rate
directly proportional to the first leadscrew. The obvious way of doing
this is to transmit rotational motion from the first lead screw to the
second, but the question is how? How, as the block moves along the
first leadscrew, can I get the rotational motion to the mechanism
mounted on the block?
I would consider using something like a telescoping universal joint
driven by gears fixed to the first leadscrew, but space retrictions
prevent this.
Since the block itself will be larger than its linear movement (about
6" versus 5"), I think I can have a shaft, one part (6") of which is
threaded as a leadscrew, and the other part (6") of which is splined.
A splined bushing on the spline shaft, mounted to the block with an
appropriate bearing (a thrust bearing?) and fastened to a gear should
work, I think. I do want to minimize backlash, and I wonder how much
the bushing would introduce.
Another option would be to use spur gear stock instead of a spline,
and have a spur gear mounted to the block and meshing with and sliding
along the length of spur gear stock. I don't think, however, that spur
gears are designed to to this, and I do think this will introduce even
more backlash than the spline/splined bushing method.
Comments and especially suggestions are welcome!
THeo