If Faraday is dead it sets up a paradox
You must truly love this word because you have been saying it since this time travelling statred at the beginning of the season, I have banged my head off too many walls when trying to convey the theory that the writers are trying to express and have been unable to even comprehend the "logic" you are trying to define.
It could be that your theory is so mind blowing that I just cant grasp it but I don't think so, you are clearly not understanding what the writers and several posters are trying to explain.
I am not saying Daniel was right or wrong about not being able to change things from 77 forward, he seems to have changed his stance from 1974 to 1977.
There is no loop/paradox, Daniel is living his present in Eloise's (his moms) past. and when we saw him in the flashbacks playing piano as a child that was his present say 1980 and Eloise's future from 1977 she always knew she would shoot him and felt she had to steer him towards the island you could see the pain in her face because she absolutely believed (incorrectly perhaps) that he HAD to go to the island, maybe if she had not steered him to the island she would not have shot him in 77, but she, for whatever reason, assumed that she had to do it, so she did.
I am not finding fun to argue this point anymore I just wish I could understand the "logic" you are using, sadly I do not think I can, it my be too intelligent for me to comprehend, or you are just thinking more abstractly than me.
Perhaps someone else who agrees with you could better explain the stance you are taking.