Firstly, I don't consider it inhumane to thin your flock. Look at it this way, in virtually all commercial egg farms, hens don't live beyond 2 or 2 1/2 years. And more often than not, the short lives they lead are not very pleasant. Your hens have had 6 quality years. I think it is more humane to make room for new layers in your flock, then to buy commercial eggs.
Second, if a 6 year old hen has completely stopped laying (and not just taking a break due to molting/winter), there may be an underlying disease or problem at work, and not just old age. Reproductive problems are very, very common in older birds and chickens are very good at hiding pain and weakness. You might want to examine them closely to feel for any masses, swelling, unusually skinny, etc. By taking out such birds now, you will spare them a slow and painful decline.
Second, if a 6 year old hen has completely stopped laying (and not just taking a break due to molting/winter), there may be an underlying disease or problem at work, and not just old age. Reproductive problems are very, very common in older birds and chickens are very good at hiding pain and weakness. You might want to examine them closely to feel for any masses, swelling, unusually skinny, etc. By taking out such birds now, you will spare them a slow and painful decline.