Super happy to hear about SWORD. If I had to guess, I'd say it's pretty certain Akainu is not in the circle of it, and that it is a faction working without the Fleet Admiral's knowledge. I'd guess that Sengoku is in charge of it, based on his profile as a strategist. This seems like something he would prepare knowing how shady the WG can be. He was clearly upset with the WG's decision to cover up the breakout of dangerous Level 6 prisoners, and clearly has had Navy spies act as pirates, as seen with Corazon.
I also think it's extremely likely that Kuzan is in SWORD as well working to help take down BB.
As for what BB wants, I have two schools of thought. One is based on the possibility that the WG decided to end the Warlord system while announcing Vegapunk's new Pacifista line. We've already seen him engineer a way to become a Warlord(originally by capturing Luffy) just to gain access to get close enough to Impel Down to recruit Level 6 prisoners. And later he tried to bargain Bonney off in return for a Navy war ship. He clearly likes to take the pieces of the WG and Navy that suit his taste. So I wouldn't be surprised if they did announce Pacifistas as the replacement of the Warlords, with BB wanting to get one to tinker with.
The other possibility is based on whatever happened with Alabasta. Clearly Cobra and Riku were able to explain what happened in their countries, but I'm wondering if Cobra maybe revealed too much. Perhaps he revealed WHY Crocodile targeted Alabasta, over the Poneglyph that reveals where Pluton is.
Now why could that POSSIBLY be what BB is going after? Because it could be that one news story that the WG REALLY doesn't want Morgans leaking. To the point of having their Cipher Pole spy reveal himself to stop. Perhaps it was revealed at the Reverie, and later was leaked to Morgans. He publishes this info, and BB decides to go to Alabasta before the Navy can.