Along with som eof the other sling suggestions, look into different ways to carry with a sling. If you are using a traditional military method you may find there are other ways to carry which are more convenient for fast shouldering or even plowing through a thicket.
I use a set-up similar to this picture
for my muzzle loader. It may not look traditional, but I can easily make sure it isn't hitting or getting caught on anything and also shoulder quickly.