Kewcumber, from what you've said about your father I think you have an absolutely enormous heart. We kind of hope, don't we, that our parents, being older and more experienced in life, will go through life with a certain amount of maturity and wisdom. Your father appears to have been elsewhere when mature wisdom was being handed out, or perhaps he swapped it for his life with his 'new' partner!
I am amazed and impressed that you can find the strength and will to forgive him for having shat on you and your whole family so badly. You are incredibly generous-hearted not to hold it against him that he didn't give you his contact details, and even to try and see his perspective. I sincerely doubt that most people would be strong enough to do that - and it requires gigantic amounts of strength.
You're right, it is the ideal to reach a place where you can say (to yourself, at least): You're no longer the kind of dad I would have wished for, but basically you're the dad I've got so I'm going to make the best of things. In a way all of us have to do that since no parent is perfect, but you've had a much, much bigger job of it than the average person. It's no wonder you seem to feel at the back (or front) of your mind that you've not quite finished that - perhaps that's in part why you still hold on to that memory of what he used to be like.
I daresay that even if your father and son were to develop a strong relationship, you will be there as a buffer to ensure that your son is protected from serious emotional harm. My family problems were nothing like yours, but I became that 'buffer' for my younger bro as we were growing up.
Ultimately, you perhaps know that your father will never mature, and so will most likely never have the strength that you possess to look himself in the eye, let alone look you in the eye, and face up to what he has done. I'm big on forgiveness and I also believe that the other side of that coin is the perpetrator learning to take full responsibility for their actions - sadly, as you said earlier, you can lead a horse to water...
You have had a dreadful example of parenting from your father, yet you would never subject anyone to the same treatment. Likewise, no matter what past experiences may have made your father weak, immature and cowardly, his responsibility as an adult, a father and a grandfather is to face up to his weaknesses, admit his failings, and bloody well grow up.