First the Modern Irish Boxers are not my only source. There are numerous books and websites that talk about Mendoza. Mendozza opened up his school in Dublin after his tour of Ireland. Try reading some books on boxing history.
Also, the old BKBoxers were first, originally fencers. This is a fact. They came out of the schools of Defense which were primarily fencing schools.
While Figg left no written records, if you ever look at the only portrait of him in a stance, he is clearly standing with a right lead. And Godfrey did describe a left lead. And desribed the left arm as a buckler. Now in English Sword and Buckler fighting, most, not all, prefered to lead with the sword, not buckler. Read Silver's Paradoxes of Defense and Breif Instructions Upon My Paradoxes. He clearly states the sword should be in the lead as it is a mmore secure defense. Mendoza's pupil did show a left lead, as that is what Mendoza prefered. He also says that what foot is in the lead should not matter, as you should be adept at both. In the pic accompanying Broughton's rules, it's just that, artwork to adorn the poster anouncing the rules.And yes, Tom Hyer and Yankee Sullivan are pictured with left leads. All this is circumstantial. As with all fencing instructors of the past, they also stressed to train for being ambidexterous. Not to mention, they taught comfort. If you are more comfortable with one over the other, go with it. Not to mention, that just because I fight right lead/left lead, I can't teach the other. It is trully a mute point. What it comes down to is comfort.
I feel that this is no longer educational, but trolling for an argument. So I will not be drawn into it. If anyone wishes to they can contact me and I will point them to the sources. Besides this is supposed to be about Irish Stick Fencing, not Pugilism.