For the first 2-4 years of an infestation, I would either release beneficial insects early such as lady bugs (beneficial insects) or
apply insecticidal soaps, Safer's Ultra Fine oil, etc .etc instead of
using Imidacloprid. If trying soaps/oil, I would apply it before the shrub leafs out and again when you see the scales hatching. All this is best if done as early in the growing season as possible (versus mid-to-late summer or in the Fall). Not sure what it will do a newly planted shrub but established ones would probably be fine. It will cause a lot of dieback on thin looking branches and the eaves that have eggs may fall and spread the problem. Last possibility and it applies to severe infestations: some people like to throw away all stems and leaves into the trash and start again from scratch.

Thanks, luis! This hydrangea is probably 9 or 10 years old (though has never flowered, grr) so is well established. I'll try the oil next year. Any point to releasing beneficial insects now, or is that better to do in, say, early to mid May while it's leafing out?

The insects would be more effective in times when you see activity/damage being done but if their cottony barrier is there, they could have split already since you cannot "see" unless you try to remove it. I would definitely make plans to start 2 weeks before you first saw something this year. Or more, depending on how the weather is.