Is it permissible for a worshiper to lead his companions in prayer, despite committing sins known only to God, and fearing that he might be late for prayer out of concern that his companions would push him forward to lead?

It is obligatory to hasten to repent from the forbidden sin. Your leading the congregational prayer after performing ghusl from janabah is permissible if you were in a state of janabah, even if there is someone among them who is better than you, because the imamate of a less virtuous person is permissible in the presence of a more virtuous one.