Thank you for your suggestions.
I think I came up with the answer, in bed, at 1.00am this morning!
I remembered I had posted a link on this forum that showed how to add a facing instead of a binding. QB member ‘willferg’ had then added 2 links to an even better method.
So I think I will get the quilting done and see what happens with the backing. If it’s ok I’ll bind as normal but if it’s pulled back a little I’ll bind it.