Dave, it is possible and easy. I use adjustable slings for a while. It is my favourite kind of slings. You need not more than 5 seconds to change the lenght of the cords.
Here is the link to my old post with pictures of that kind sling, made for snowballs and tennisballs:
http://slinging.org/forum/YaBB.pl?num=1171155835/23#23There are used two sliding knots. You can easily move them with fingers to a desired location but when you sling they are stable. I use the "clove hitch". The endings of the strings are protected by a lighter in a way, which makes impossible unbinding them. That knot works well for the kind of string I use. You may also experiment with other kinds of sliding knots. For the finger loop the "double bowline" os used.
The mentioned knots you can see on the webpage linked below. I'm not sure the names used there are correct. Anyway the pictures say all. Here is the link:
http://www.geocities.com/a1marine/Pagethre.htmlGood luck. Please let me to know how it works for you.
Jurek