Stepping through seems to take me just 10 seconds along the time-line - rather
slow for a long production. I have 5-minute-ish chapters made, and want to
jump along them.

A . will advance one frame. Using the left and right arrows jumps 10 seconds. Using the up and down arrows jumps 60 seconds. Using page-up and page-down will advance 10 minutes. Using ! and @ steps throught chapters, I think.

I can't find any snapshot tool, and using ksnapshot seems
to result in either a blank blue screen or a jig-saw series of part-screens,
overwriting previously saved unrelated pngs. I've never seen behaviour like
this before.

I had this problem when trying to play videos on a TV via s-video. There is probably a better way to do this, but opening the video once, pausing it, then opening it again from a separate terminal will cause the video in the second window to be captured with various print screen programs.

looking now at
man mplayer
/screenshot
(then 'n' to cycle through)

This seems to give useful information, but using the 's' key as suggested didn't work for me.

Good Luck

--
Dylan