Even after the triple denial, Christ still loved Peter, and did not reject him.
In fact, according to the dictates of Keyes' faith, Christ still set Peter as the head of His church.
Incorrect. The two are separate issues.
The orthodox understanding is while Christ still loved Peter, His three "Do You love Me"s were prerequisite to restoring Peter.
Also note that in the same exchange Christ tells Peter his manner of death as opposed to the open question of John's death. Not conclusive, but strong reason to infer the denials and the manner of death are related, despite Peter's return to Grace.