It can be acquired a good accuracy with any length of sling, but it is easier with short ones, and greater the accuracy achieved. It is known that the Balearic slingers of the antiquity used three slings of different length according to the effective range. They wear the short sling around the head, the longer around the waist and the medium one  in the hand, that should be the more used. One assumes that the short shots, to an individual person, require greater precision than shoting a distant multitude.
The length of the slings must be mesured in relation to the arm of the slinger. A sling of medium type, for all uses, must extend from the end of the fingers to the shoulder, and a precision sling from the end of the fingers to the elbow. For my arm, that are 75 cm and 45 cm (the sling folded), respectively.

As far as the long sling, to obtain range, it must be measured in relation to the projectile. First, the longer the sling better, but it is necessary here to consider the purpose. We enter the subject of Yurek, to optimize the sling for range.
In military use the purpose is to achieve a strong impact fron great distance on a mass of people. For that reason great projectiles are used that allow  to use very long slings. But in modern contest the purpose is only range, and as I said to Yurek I think that it´s more advantageous to use small projectiles. With this type of projectiles a too long sling will have much air drag and its weight in relation to the projectile would be considerable. The spinning wouldn´t be effective and the transfer of muscular energy would be bad.
The subject is worthy of a study and experimentation.

Well, after all, being the sling a  simple weapon, it has its complication if we want to beat records  

The ancient Balearic slingers were warriors and found more useful at war to take three slings of different length according to the range that a sling of adjustable length. It was faster in the battle to change the sling that to fit its length, and in addition an adjustable sling offers more air drag and more weight. The more simple and light the sling, better. An adjustable sling really can be useful at the beginning of learning to try different lengths without having to construct different slings, but once selected the lengths that are more comfortable for you the best thing is to make the slings of fixed length. The Balearic slingers could have used an only sling for all uses as other people did, and then they had used a sling of average length, that is worth for everything with good general performance. The fact that they used three different slings talk to us of the great performance of their shooting.
The weight of the projectiles could be the same for the three slings because they looked for a destructive effect when they used stones. Later they would use glandes also. And as far as the slinging style it had to be the same too, according the old texts: three turns round over the head before launching.

I know you are an unconditional fan of the underhand style, which limits a little the length of the sling, but using the same style you can spin a little inclined and thus to use longer slings. But if you want to get good ranges is necessary that the arm goes back streched out in the last spin, and from there to cast strongly, as Yurek said to you in other thread ...  As for accuracy with this style I think you have to use heavy projectiles and  as standardized as posible, if not the shots will go up and down the target. Heart... and constant practice