The Iroquois Confederacy as a model for the US constitution: symbolism of the arrows

The Iroquois tell a story about how they were at war until the Peacemaker brought the original Five Nations together: "he demonstrated the confederacy’s strength in unity by first taking one arrow and breaking it, then bundling five arrows together and showing how the bundle could not be broken." The Iroquois confederacy was cited as an example to emulate by founding fathers such as Benjamin Franklin, and the arrows still appear today in places such as the Onondaga seal and the 2010 US $1 coin. The Onondaga added a 6th arrow when the Tuscarora joined in 1722.
In August 1775, the Continental Congress sent a delegation to Albany to ask the Six Nations of the Iroquois to stay neutral in the war with the British. John Hancock, president of the Congress, quoted the Iroquois story: “…They have frequently taken a single arrow and said, children, see how easy it is broken, then they have tied twelve together with strong cords – and our strongest men could not break them. See, said they, this is what the Six Nations mean. Divided a single man may destroy you – united, you are a match for the whole world.”
The original design for the Great Seal of the United States by Francis Hopkinson in 1780 shows lady liberty holding the olive branch and a native american warrier with a bow and arrows.
When Charles Thomson finalized the design in 1782, he kept the bundle of arrows. Just as the Iroquois used 5 arrows to symbolize their 5 nations, the great seal used 13 arrows to symbolize the 13 states. You can see this today on the one dollar bill. Why do you think Thompson switched the olive branch to the right side?