Either people simply began to attribute all manner of teachings and sayings to a Jesus, whether Jewish or Greek cynic sage type, Q and Thomas sayings and teachings as well as from the OT, or all these teachings were distinctly remembered as coming from a particular Jesus of the early 1st century which no one wrote down until the end of the century, but perfectly preserved in their memories and passed on for 60+ years as it has been suggested by a certain Oberon. Occam's razor anybody?
1. Your Occam's razor reflects a lack of understanding not only on the nature of orality but more importantly on the culture of the first century and the nature of ancient texts. We are EXTREMELY lucky that various authors, including Mark, Matthew, Luke and John, began recording in WRITING the Jesus tradition as early as c. 35+ years after Jesus' mission. We don't have ANYTHING near that for the vast majority of ancient teachers. Pythagoras, Hillel, Shammai, the Teacher of Righteousness, John the Baptist, and many, many other famous and very influential teachers have barely any mention anywhere, or are only mentioned in a substantial biography 7 centuries or so later.
Yet Jesus has 4 complete lives, as well a numerous other references to his teachings, within a lifetime or two of his mission.
2. If people simply attributed any all manner of sayings to Jesus, then independent sources (Q. Mark, Paul, John, and according to you 1 Clement) would vary widely, more than they agree. Yet we don't see that. Jesus' teaching's are fairly consistently recorded in these sources.
3. The oral tradition began to take written form as early as Paul, and was shortly followed by Mark. I am not arguing that the oral tradition remained well preserved 60+ years after Jesus' death. That is (in essence) your argument, by arguing that 1 Clement independently records Jesus' teachings. I am arguing that 1 Clement used the synoptics.
Occam's Razor: We have a number of lines in 1 Clement that are similar to lines found in the synoptics. Either we can suppose that 1 Clement, 60+ years after Jesus' mission, and while the gospel texts are beginning to dominate, independently had access to an oral tradition that faithfully preserved teachings of Jesus recorded in the synoptics, OR we can accept the simpler solution: 1 Clement used the synoptics.
4. When there is a question in ancient history on whether a various traditions are based off of the same tradition, it is because they are attributed to different names and the sources disagree so vastly. For example, there are a number of references to an Antiphon whom most classicists agree are the same person: Antiphon the Sophist, Antiphon of Ramnus, and Antiophon the Orator, usually referred to in texts simply as Antiphon. We have a number of speeches attributed to Antiphon, as well as philosophic fragments, and a number of references, but accounts disagree and the speeches are not only stylistically different from each other, they don't at all resemble the philosophy, either in form or in belief system. Yet most classicists argue that all of these are the same antiphon. The differences in the texts attributed to him are explained by their different genres. The differences in titles are explained by the focus of the person referencing antiphon. And so forth.
We have no such evidence for multiple different people behind the jesus tradition. Q, the earliest record of sayings, attributes everything to Jesus Christ. Paul also calls him Jesus Christ, as does everyone else, even Josephus (who changes it to "called Christ"). The only other titles (e.g. Jesus of Nazareth) are given in works which ALSO refer to Jesus christ. Not only that, the teachings attributed to Jesus are far more similar than, for example, the sources attributed to Antiphon. We have no reason to assume that people simply began to attribute sayings to a person who was eventually thought to be some "jesus" and every reason to doubt this.