Bilstein HD and Bilstein Sport are both monotube dampers. Judging by the photos from Shock Warehouse (who post actual product photos, not stock images), they're an inverted design too.
Both of these indicate a premium damper, not an OE replacement like KYB or Sachs would be. Bilstein Toruing is Bilstein's answer to an OE replacement part. All three are generic twin-tube designs, just like the ones Mazda put under the car.
I guess it's all up to what type of part you want and how much you're willing to pay. If you want a more inexpensive OE replacement damper that will perform like the struts you're taking off, you have those options in the KYB or Sachs. A Bilstein damper will cost you more, but it's a premium part.
I've actually owned all three of the options you're proposing (and then some). I installed a replacement set of KYB GR-2 on a Subaru. I wasn't any more impressed with them than any other OE replacement, like Monroe. I've also used KYB AGX adjustable dampers on a Miata. Completely not impressed. Junk is a good adjective. They were replaced in less than a year with Koni yellows and sold to some unlucky person from Ohio. My current vehicle has OE Sachs dampers on it. One is leaking. My only replacement options are Monroe or Sachs. I will likely replace them with another round of Sachs, given the choice between that and Monroe. My last vehicle had OE Bilsteins that were replaced with Bilstein HD. There was nothing wrong with the OE Bilstein, but I wasn't happy with the low speed valving. The HD variety fixed that.
Given your leanings, buy the Bilsteins. You won't be disappointed. I still stand by my recommendation of trying the Koni FSD. It is a twin-tube design, but uses some pretty cool technology with the valving.
