Yay a fellow MBTI enthusiast
I agree with your analysis for Tim and Jason but for Dick I think he's an ENFJ. He has the traits of the NF temperament more than the SJ one. And Damian was definitely written by Morrison to be an INTJ and it's carried on into Supersons and Teen Titans. Sorry but no way he's an INFP. He has no traits of the NF temperament nor does he exhibit Fi-dom or Ne-dom characteristics. INTJs instead have Ni, Te as their dominant functions but do have Fi as their tertiary which makes them come off as insecure and idealistic in a very quiet way. They'll almost never tell you what they're feeling unless you're someone super close to them. Most of the time they don't even like to recognize what they're feeling, instead pushing it off and distracting themselves with other more efficient and effective things. In contrast, I think Jonathan Kent might be an INFP but he's too young for me to tell for sure but he's definitely an NF (like Superman). There's not really a whole lot of NF characters in the Batman universe. The only ones I can think of are Dick (ENFJ) Alfred (INFJ), Mr. Freeze (INFP) and the Ventriloquist (INFP)
Bruce is a big one I see mistyped too much. A lot of people think he fits into the INTJ catagory because he literally nails all the sterotypes of one. He's actually an ISTJ. Si-dom is very detail oriented, over planning things, great memory, "by the book" function. Will never try to assume to know the big picture before having sufficent evidence. Te as their second function allows them to rely on facts and proven methods. Tertiary Fi where they make their moral 'laws'. Inferior Ne for ISTJs is a funny one. They will use it in times of stress and make veryyy reaching statements about how they perceive things to be. The slippery-slope argument he uses when people ask him why he doesn't kill is literally all derived from this function. He will become a morally bad person (Fi black and white thinking) if he breaks his rule (Si)
The Si-Fi loop in ISTJs is literally why the story of Batman was made in the first place. The sensory and memory details of the night his parents were killed is what sends him down spiraling to stop other people from feeling the way he did that night. He's very stuck in that memory because he remembers the feelings of it too vividly. He takes in other kids who lost their parents because he projects that feeling he has onto them and understands how they feel. An INTJ in this situation would honestly just mourn and move on. Because they are big picture oriented (Ni-doms), they understand that death is a nature part of life. Yes parents are important and they might want revenge but ultimately, it wouldn't drive them to try to make a change in the city because of one night. Their driving force would be trying to change the corruption of the city into something positive with reliance on remembering the pain of what they went through. Damian almost never uses his time when he was with the League of Assasins as a motivater for his crimefighting ways, barely even references it most of the time but he still ends up with the same goal that his father had.
The big thing between ISTJs and INTJs is that one of them will stick to proven methods and rules extremely firmly (almost to the point that it's like talking to a brick wall that you're asking to move) often times without any logical ties to the rules because their decision making system comes from Si-Fi, while the other will take an idea and tweak it constantly until they come up with an absolute truth. Batman's no killing rule comes from his Si-Fi loop. Whereas someone like Jason who has Fi-Se makes his moral judgments (dominant Fi) based on his own experiences (Se). Bruce has never experience being murdered so he could never understand why Jason kills. Damian has never had a rule that he has made up. Instead he follows what Bruce says because he still wants his approval (tertiary Fi) but if left to his own devices he'd kill on a case-by-case basis. Irredeemables like the Joker would just be killed off in order to stop the corruption of the city.
Sorry this is very long >< I really enjoy discussing MBTI though and have been using it to type people for 6 years now. It's a very useful tool for social communication and really fun