Jesus almost certainly claimed that he and his twelve disciples were going to rule over the new kingdom of God

Prove it.

We can be pretty sure because Judas then goes and betrays him, which we’re also very certain actually happened.

Prove it. Also explain why Paul doesn’t seem to know about it.

Finally, Jesus probably actually was from Nazareth, because that town was basically like being from nowhere in those days. It would be strange to invent a story about a god and have them come from a podunk place, especially in those days where class mobility didn’t exist.

Not if you held to a doctrine that “the last shall be first and the first shall be last”. A very popular theme in Jewish mysticism. Plus it would explain why there is no Jesus family around to claim the throne, except for James.

Furthermore, we can be pretty certain John the Baptist really did baptize Jesus. My understanding of why is a bit more limited but basically that action put John in a higher position of authority than Jesus which would have been a big issue. Scholars think Jesus was originally a disciple of John.

Criteria of embarrassment is the term you are looking for. That thing almost never used outside of biblical studies since it is a weak argument. It doesn’t work here. John the Baptist was more well known than Jesus was at the time of Mark. By attaching Jesus to him it was just another form of name dropping. Additionally Mark has John still humbled in the role. So even less embarrassing for Christianity.