So you'd say that the Artefact issue is a mere detail? I mean, if I was Order and were to chose between the major "pirate" groups to ally with for bulk because the Houses governments couldn't be trusted at the time and there was the need to actively fight them I'd go for the Hessians.
I mean, the Outcasts, as far as the Order is concerned, are in bed with their primary enemy, so that would be a crazy (at best) option.
The Corsairs indiscriminately distribute what could very well be Nomad related materials throughout House space, not to mention they're directly exposed to it throughout their lives.
So, you're left with the Hessians. I'd say that their "alliance" with the Outcasts exists much more because of the whole (Corsair vs Outcasts two sides of the war thing they did with all pirate factions in Sirius) than anything with more substance. AFAIK Hessians have no involvement in the Cardamine cartel (or do they?). So, for that matter, the Hessians would configure a less dangerous, or at least less uncertain, base of strength for the Order.
Also I'm somewhat bugged by the fact that people who set out to defend the human race against the Nomads would just chose to oversee Artefact smuggling. It's REALLY strange. AFAIK, the Liberty government just outlawed Artefacts because it wanted them for itself, so they could study them and harness whatever powers they might discover. How would the Order ignore that?