I give you my thoughts. First off, the first tree that he calls Hardy Chicago, isn't. The reason behind my answer is his description of fruit. HC is not a large fig. To be honest, i read the article without looking at the leaves. My first guess is Brown Turkey, but as I said didn't match the leaf. Some one will chime in and give your proper ID. Secondly, these trees will have to be pruned back to survive a move, which moving will stunt its growth for a year. If trees are common figs, you can get them to grow that much in 3 to 4 years. My point is you will lose a year from transplant so why not just start your own. Thirdly, this person more then likely has asked a landscaper to remove and saw how much the bill was and is trying to get rid of plus make a lot of money. I would not offer over 50.00 if you have to dig out, matter of fact i would probably offer to remove for him at no cost. If you find you would like to root some cuttings from these trees, offer him some money for a few branches.
luke