In terms of pulling aggro from the tank, melee DPS will pull aggro from the tank if they are at 110% above the tank's current threat. Range DPS will pull at 130%.
Most melee will actually be at outside of the 110% range, especially on the bigger bosses. Unless they're explicitly hugging the boss, they'll require 130% just like the ranged.
There has been some theorycrafting for the exact range to be at for 130% to apply and this was found to be at 2.76m.
It's not theorycrafting. It's experimentation. Theorycrafting revolves around theory. Experimentation actually involves going in game and figuring out what's going on.
And your "theorycrafting" isn't even correct. The melee range for threat is based off of being within 4m of the center of the target's model; for comparison, melee range for attacks is 4m of the outside of the target's model (the range listed in the UI is actually the range from the outside of the target's model). The reason why you found 2.76m to be the "sweet spot" is because the target dummy has a model radius of 1.24m.