Thanks to everyone for their excellent advice – very helpful. This run has been a dream of mine for several years. I think I could do it in 21-28 days of good effort.
Yes, I posted on mds.co.uk – I ran the Marathon des Sables this spring – lots of fun… I'll check out the fell runner site – great tip!
I could be wrong, but I don't think you'd need much of a support team for the GR10 – there are huts along the route. I would guess some minimal supplies in a pack, perhaps a package in post restante at the midway point, and voila! – easy (oops, pretty sure I'm going to regret saying that some day).
Expedition running and hiking are not so different. You still get to see all of the great views, to relax at scenic points (in fact, you get more time potentially, 'cos your travel time is so much less).
Interesting the reference to the GR1 (Diagonale des Fous) – thinking about racing that this fall. That is a very hard course.
So it seems doable to run the GR10 – I have the Cicerone guide book, but it's always useful to get multiple opinions. I looked at the HRP, but the trail looks trickier, and resupply more tenuous.