Hydrangea are generally not propagated by splitting / division!

Your best course of action now is to take some tip cuttings ( I did mine yesterday) and hope that these will root.

Take plenty non flowering tip cuttings ( to allow for losses)

The ones I took were around 6" (150mm) long although shorter ones should be OK.

A lot depends upon what is available on the plant!

What you need on each cutting is at least one leaf node in the soil, I chose to have two hence the longer length.

My theory is that this will double my chances of rooting as the new roots come from a leaf node!

This link and its associated links might help;

http://www.thegardenersalmanac.co.uk/Data/Hydrangea/Hydrangea.htm

Sorry TG but Annabelle is best propagated in Spring from the new growth unlike H. macrophylla types which can be done now from non-flowering shoots.
If you can find a non flowering shoot you might be able to get it to root in the normal fashion, but success is hard.
If the shrub has more than one stem coming from below ground level (mine has a dozen or more) you might be able to find a small one with roots which could be detached.

What prompted my answer Owdboggy, was the fact that they were moving within the next few weeks.

Plus as I mentioned; "A lot depends upon what is available on the plant!"

I take your point about growth similar to suckers, but again a lot depends upon what is available on the plant!"

I'm not normally a pessimist, and believe very much in the adage" nothing ventured nothing gained" but I have my doubts

Perhaps it might be better digging up the whole plant (if this is practicle)and heel it in, or pot it up till a suitable planting time.

Bit 'iffy' this one don't you think?

If you are not moving too far away maybe you could come to an arrangement with the buyer to take it later in the year? My Annabel sent out runners some distance from the parent so it was easy to detach one and pot it up, but I did this while it was dormant.

I have tried cuttings from Annabelle at this time of year and they did nothing whereas the Spring ones all rooted very easily. I have also managed to take rooted pieces from the plant, but again before flowering not as now when the plants are in full growth.
As you say though, nothing ventured...............Bottom heat and high humidity might work.