As I think more about it, maybe another approach will work.

There is 5 feet of pipe between the house and the walkway, 5 feet under
the walkway, and 12-15 feet more to the manifold.

1. I dig on both sides of the walkway until all the pipe is exposed.
2. I cut and remove the section between the walkway and the house, and
cover the exposed end to prevent soil from entering during step 5.
3. I cut the pipe on other side of the walkway, leaving a 1-foot "stub,"
and remove the pipe all the way to the manifold.
4. I connect the replacement pipe to this stub with an ordinary
lawn-pipe connector that slips inside both ends. (I pour hot water on
the ends of the pipe to make inserting the connector easier.)
5. I simply push the new pipe under the walkway toward the house and cut
off the old section after it emerges.

Of course there will be the friction of the soil to overcome. But the
break is under the walkway, so before starting the above, I'll simply
turn on the water for a couple of seconds so the water coming out of the
break will act as a lubricant.

Have I overlooked something?

Ray