Thanks for the reply. I have moved the immediateRender to the 'to' properties (seems strange, my understanding of immediateRender is that it applies to the 'from' properties but it does seem to work either way).
I set autoAlpha to 1 in the staggerFromTo 'from' properties to ensure that a previously faded box would be fully visible before the slide started. I don't want that Tween to then change the autoAlpha, the autoAlpha has to change in the following Tween (after the slide has moved left), hence it's in the staggerTo and the to of the Tweens that act on the box that precedes the sliding one in the sequence.
I can see your solution works - thank you - but in my understanding a 'set' at that point in the timeline is exactly the same as a 'from' with immediateRender = false. So in your solution, at that point in the timeline the autoAlpha is set to 0, and in my original, the 'from' properties of the fromTo set autoAlpha to 0 at exactly the same point and so the resume should work the same in both cases. If you have time to explain what's wrong with my thinking then that would be useful for future reference, if not then I will just gratefully accept your working solution!