The sentence you quote does have a certain literary flavour about it but I would agree ii is grammatically correct. Let me try to say it in other words: I think I am justified in continuing to find the child still alive mainly because of the great benefit that would be gained if I was successful.
The unusual use of ‘obtain’ is probably the part that you found confusing. Usually ‘obtain’ is another word for ‘get’ or ‘acquire’ but here it is used without an object to mean ‘exist’