You can get a bit more than 3" with 90* rotation.
A 3" arm at 90* rotation gives you the square root of 18, or 4.24 inches of travel if you have your leads set at the correct angle to the arm. Since most people use a one:two reverse purchase, that can be as much as 8.5" of sheet travel.
I have thought about using a cam type of servo arm to get more travel with an arm type servo. Done right, you can get more travel in some parts of the rotation, and less in others, for fine adjustments.
Remember, you can also adjust where you attach your sheets to the booms to make up for more, or less sheet movement. The servo is going to do a certain amount of work (it's torque rating) and it does not care if it pulls in 20" of line or 2" of line over it's rotation. You will lose some of the torque every time you change direction of the sheet, through pulleys. Some have said as much as 5% every time you reverse the direction!
That being said, you could use a 1.5" arm and no purchase system, but your sheet would have to attach to the booms about two inches from the pivot point/gooseneck! it would be hard to make small adjustments to trim at that close distance.