I think this discussion has lagged on beyond what is beneficial to developing mutual understanding so I will withdraw from it. I'll yield to the point of institutionalized pedestry, not because I agree or consider it moral, but because I don't think we are going to form any consensus with discussion and I think it will make a good place to conclude. I think we can agree that if assuming that much of the problem were systematic, then the fact that a pedophile knows that choosing to have sex with a child could cause the child to be harmed through the systematic process, if not by their own behavior, is still an exploitation. I say that not because I agree with you that it is a systematic problem, but hypothetically if it were, then a pedophile would still knowingly be harming a child by putting them through that system.
So in essence, if pedophiles want change, they will have to go about it the way every group has, and I highly doubt they are going to meet a sympathetic society for all the reasons I have mentioned and more. Furthermore, society is very adamant about not reshaping itself to accommodate small minorities as you can witness with the resistance to allow same sex marriage, so the likelihood is very small that society will reshape itself since fewer than a 1/10th of a percent of people are pedophiles. The accepted numbers is that 5-8% of the population is gay and bisexual and the arguments for homosexuality are considerably stronger given that it only involves adults, and homosexual couples can provide a measurable benefit to society, and yet it is still considerably difficult to obtain tolerance and recognition. Furthermore, as I've stated before, science is continually developing its understanding of child psychology and development, and there is nothing in those studies which suggests that an institution of pedestry would benefit children. However, there are 8 to 10 million children of gay parents and same sex couples in this country who would benefit from greater societal acceptance of homosexuality and same sex marriage. The latest 25 years of research of the parenting abilities of same sex couples further substantiates that argument.
As such, you aren't going to get anywhere by comparing homosexuality to pedophila because, they are not only fundamentally different issues, but homosexuality can actually provide a benefit to society, whereas pedophilia is purely about self indulgence.
I stand by my position that pedophilia is generally immoral, exploitative, coercive, and a disorder. Howvever, I will concede that our values and reasoning differ on this issue and you are entitled to your beliefs.