Sounds like you guys really cared for that dog to spend that much on surgery! wow!
Well I would say just make his time as comfortable as possible.
My lab cross is going to be 6 and she already has some bad hips, I cant imagine she'll make it to 13 without surgery.
I cant imagine what your going through, but I would say just try not to hold onto him just because of your feelings, his his quality of life is poor then he is not happy. As far as making it "tear free" that just isnt possible. Death is what comes to having pets. Its the hardest part of life and its just something that must be done.
I hope you and your family cope with this well and good luck!