Other than the last question, it's a matter of personal preference.
This article about this kind of meat is linked in the sticky in this forum. If you haven't already found it, you should definitely read it. Yes, the meat will be a bit tougher than store bought, though personally I wouldn't call it gamey. Meat from dual purpose (DP) birds is always firmer than store bought chicken, even at a good age for tender meat, around 14-20 weeks. Also, the taste is different, even at that age. Many who eat this meat regularly will tell you that the best chicken soup or broth (or chicken and dumplings) by far is from an older hen. Also, if you wouldn't consider processing your own, you might find eating them nearly as difficult. The first time I processed mine, many years ago, I tried to eat it and in the end gave the meat away to a friend experienced in this kind of meat; she very much appreciated it! The problem was definitely between my ears.
Another thought. My 9 hens give me about 5 eggs a day, about 7 last summer, and all but one are older than 1.5 years; a few are 4 years old. It's likely that 1 or 2 don't lay at all or only rarely, so if I wanted the flock to be more efficient, it would be simple enough to separate each one for a week or two and find out. The eggs of course are huge.
So little meat results from processing one bird, compared to something like a cow or pig, that it is quite difficult to find someone willing to process for you. I would look for an old farmer locally, or perhaps ask at your feed store. "Spent" hens or unwanted roosters usually sell for $5 - $10 live, if you can even find a buyer, so charging to process just isn't going to be profitable.