I have a Safari Ching sling and have practiced with it using several rifles. I am also familiar with the military sling as I compete service rifle. The Ching and military slings work by putting you and the rifle under tension; the military sling much more so.
Both slings make my hold steadier in the seated and prone positions. Offhand I found little improvement using any sling (slings aren't even allowed in competition in offhand strings) but that could just be me. The problem I found with slings that put tension on the rifle is they share one common trait: using them changes my point of impact as compared to that from a bench or using shooting sticks. For me using the Ching sling with enough tension to make a marked improvement in rifle steadiness lowered my POI by 3 MOA as compared with shooting from a benchrest or shooting from a bipod/sticks. I did not notice a significant change in windage while using the Ching sling but I have a lot of practice with proper use of the military sling or I just got lucky
.
Everyone's different. Perhaps you're able to remember what the change in POI is with & without a sling or you don't even experience it. What I finally opted to do was
not use a sling for the benefit of steadying my aim and the resultant change in POI
while hunting.
A Ching sling (or one that's similar) is worth a try but I suggest you do the work and compare your POI with and without a sling in the positions you expect to use while hunting.