Breach of contract will be extremely hard to prove all they would need is one security officer say that he received a complaint about the people at the booth.

Breach of contract need not be limited to the cause of their ejection as it could include the manner in which they were ejected. In this piece they state:

This incident contravenes the published policies and procedures outlined in Calgary Expo’s materials. Their own policies specifically state that verbal warnings and requests to cease the behavior should be the first step in the process of dealing with complaints about exhibitors and attendees.

If that is the case then it could be that they were removed in a manner not allowed under their exhibitor agreement. There may be some weasel clauses, but if their agreement is not sufficiently clear or it was otherwise mishandled then it may give them a position to argue breach of contract or wrongful termination of the contract.

Also how are you planning on getting around an accusation of applying under false pretenses?

Have you been following this situation very closely? This one is fairly obvious. While their exhibitor name changed several times, these arrangements were made weeks in advance. Only other thing they had against HBB was some rather obvious tongue-in-cheek remarks about deviously pretending to be nerds for decades.

Also businesses have the right to refuse service to anyone.

This actually isn't true as you can sue someone for refusing service if they do not have reasonable cause. It doesn't just apply to discrimination based on identity.

You won't get any ground here.

They may be phrasing it badly. I definitely think the pieces in The Mary Sue and Raw Story would qualify under injurious falsehood. Neither of those outlets merely reprinted unfounded accusations, but made their own inflammatory false attacks on the Honey Badgers.

And this doesn't make any sense. A court can not cleanse a person and organizations name publicly and it most definitely can not force a convention or any other kind of events to allow HBB to participate.

They can actually do both. If a court finds in favor of the Honey Badgers on the injurious falsehood and breach of contract claims, it will publicly exonerate them. Courts also force others to provide services all the time. Whether that will happen in this case even with a victory is uncertain. If the Honey Badgers still succeed in their suit, then they will definitely be compensated for any expected sales that are lost due to the ban.