John the Baptist

[John V]

That we're both biased on this issue.

Skepticism isn't a bias. It's critical thinking applied to another person's bias.

In that case, "immediately" in Mark reads to me as "immediately after the wedding in John," and I retract my concession of that conflict.

And with that, we're done.

I'm not done. You did identify a single discrepancy of a single word - immediately. However, check the usage of the underlying Greek word. When the context indicates time, it's translated as "immediately" or something similar. When the context involves geography, it's translated "straight." The context is that Jesus was going to the desert, so it could be that Mark was indicating he took a straight path to the desert, and translators are incorrect in interpreting it as a time reference in this verse.