"If scientific reasoning is merely Bayesian,"

Scientific reasoning is an imperfect approximation of Bayesian reasoning. Using your geometric analogy, science is the process of sketching a circle, while Bayesian reasoning is a compass.

"It seems to me that it is easy to represent strict standards of evidence within looser ones, but not vice versa."

If you already understand the strict standard, it's usually easy to understand the looser standard, but not vice-versa. Physicists would have a much easier time writing literature papers than literary theorists would writing physics papers.

"The frequency of 'Bayesian reasoners' mistaking data for evidence on this site should serve as example enough."

Data, assuming it's not totally random, is always evidence for *some* theory. Of course, not all data is evidence for every theory.