In Apples Logic software you can select a range of notes in a MIDI passage and stretch or reduce their overall execution time with respect to the grid, all subsequent events being moved relative to the end marker of the selection. In this way it’s possible to take a live MIDI recording, say of a piano performance, made without the use of a metronome and make it fit the GRID, thereby syncing in with other tracks or events.
What I want to know is - is the absolute reverse of this possible in any software? Is it possible to move key GRID timeline events (star of bars and note sub-divisions etc,) so that it can float over and sync with the same events in an audio recording or MIDI passage?

You can do it if you render your MIDI piano performance (made without the use of a metronome) into audio first. (or just start with any audio, first).

Most, if not all of the DAWs out there have a function that will analyse a section of audio and map discrete tempo changes to it.  This type of function won’t change or damage the audio itself, but will map hundreds of tempo change nodes throughout your section of audio until it ends, some often spaced very close together.  The whole grid for your project will then follow those tempo changes, meaning that any other parts you add as MIDI data later on, will also follow those discrete tempo changes and keep to them.

So, it’s a dependancy kind of thing.

These types of functions work best when you trim your audio very tightly to the very first transient and preferably on a down beat, making sure there’s no empty space before you analyse it.  They can be quite finicky and usually prefer to be fed a drum pattern as opposed to just a piano part, because the transients are much easier to identify and map for a drum pattern, but you’ll be amazed at what they can map!

I think it’s called Smart Tempo in Logic. 
Pro Tools has Beat Detective.
Cubase is something like Tempo Detection?
Ableton is called Warp, I think? 

Hopefully users of Cubase or Ableton can chime in and set me straight.

So, yes, these functions make the grid follow your looser/free musical timings, but they analyse audio (and not MIDI) in order to do it.

You may run in to problems if you wish to match other, unrelated audio to your project, but there are tools that will let you manipulate the spacing of transients in an audio file and quantize them too.

Logic, as an example, has a transient editing mode. I’m sure all the major DAWs do something similar.

Thanks ‘philwoodmusic’, your comprehensive reply and use of the correct terminology across various DAWs enabled me to locate all the information I needed to carry out the task I outlined. I’m now fully charged with all the techniques necessary!
Thanks again. 🙂

You’re welcome.

Best of luck in your quest.