I haven't transplanted many hydrangeas. I dig a lot up in the fall and overwinter them, but they won't go back into the ground until spring.

I transplanted a large oakleaf in the spring once and it wasn't too happy about it. It was large and that was part of the problem, but it also had roots that were more woody than many other plants and didn't have much in the way of smaller fibrous roots if that makes sense.

I've dug up macrophyllas in the spring and put them into pots. They weren't that quick to recover and were not nearly as robust that first summer as the ones left behind. The root ball also didn't have a whole lot of the small fibrous roots (there must be a better term for the type of roots I'm trying to suggest to you)

I've been moving a lot of arborescens over the years. Some I move in the spring, some fall, some summer, and I haven't really focused on how well the different ones do. But they have become established after a first year setback. The roots of these are also more wooody and don't really come out as a tight rootball, but instead they remind you of lots of underground stems. But if you throw a bunch into a hole, they do fine after languishing the first year.

Bottom line? I think I'd wait until spring.

Good luck. Hay.