when you take it to the butcher they hang it in a cooler for a few days,the slim you are talking about gets real dry. being dry it is not slick.I know this because a friend has a shop and I watch them (and help some.)
water is what causes this slim. the only way to get it off at home is to do as you have been doing.the dryer you keep it the better you can get it off.

the more time you spend on your meat,the better eating you will have.

I am not a hunter I am a whitetail population reduction specialest

remember keep your back to the sun, your knife sharp, and your powder dry.