Over-pruning it should make it floppy - just the opposite. If the flower heads are too heavy for the stem to support, you can cut them back so they flop less or just accept they'll flop.

I've got a ton of different kids of hydrangeas and have no problem cutting back those that get large in order to keep them at a manageable size and to shape them they way I want (one, in particular, intrudes on a path if I don't keep it cut back. Another would grow over the HVAC unit outside).

I've never heard of anyone 'dividing' the root ball of a hydrangea. It's just not that kind of a plant. I've propagated them by taking cuttings.....

You can certainly move it but if it has a huge rootball it might be more tedious. I gave away several hydrangeas to my neighbors and they are all flourishing but they were not enormous when they were transplanted.

Wander into a decent nursery and ask this question. I don’t think you can divide. I think you can bury a few branches, removing the leaves and making sure the node is in the dirt, and it will re-root for next spring.

So much contradictory advice online—does anyone have personal experience? This hydrangea is huge, totally disproportionate to the rest of the bed it’s in, and very floppy (possibly from over pruning?).

What are my options? Could I divide it? Or at least move it somewhere it won’t stand out that much? It’s practically a tree. Should I heavily prune it to make it easier? So confused 🙃