When you say that the stems are like regular statice, do you mean they have ridges -- but maybe even a little more pronounced than the ones on statice stems? That's a strong sign that it is Ammobium alatum. The alatum part of the Latin means "winged" and refers to those thin ridges on the stems. (The common name is "winged everlasting.")

The flowers should be about the size of your thumbnail or a bit smaller, flowers very double, a little like pearly everlasting that's opened up. We use it a lot for wreaths, too.

It's getting hard to find anything but the "Bikini" strain on this, which is "more compact" and uniform than the straight species, which you can still get from J.L. Hudson and Chiltern and heaven knows which Canadian sources. It's easy to raise from seed and, as you know, has a long season if you keep it picked.