Interesting question, Francis Higgins (Sham Squire?).
The informer William Bird, aka John Smith, made reference to the "Brown Square Boys" in one of 1796 communications. He fled to Liverpool because he believed his activities had been rumbled and he feared for his safety. While James Hope lived in the area for a time, I think that Alexander's was a meeting place for United Irishmen from different parts of the town. Hope denied all rumours of a United Irish assassination committee, as did the State Prisoners who gave evidence before the Secrecy Committees of the Irish Lords and Commons. Hope also said that leading members of the Society disapproved. Evidence would suggest otherwise, although I suspect it was not a proactive policy of assassination, rather the elimination of those who threatened to undermine the United Irishmen by becoming informers.
Friar Phillips is a case in point and his death in January 1796 marked the start of a number of killings and attempted assassinations. The most interesting are the murder of Joseph Connell (Connolly) of the Limerick City Militia and the attempted killing of Sgt John Lee who worked under Captain MacNevin based in Carrickfegus.
Bigger is an interesting source of evidence, if a bit hit and miss. This is a fascinating topic - good luck with your research.