Is it being properly cautious, if experts disagree about something, to choose some intermediate probability for that proposition and treat that as the best that you can do, as a non-expert, at estimating the probability on all the public evidence?

Not really. Such false caution can result in giving undue weight to opinions governed by faulty methodology and kept in place by merely sociological forces. In New Testament studies, such false caution also doesn't take due regard to the way that poor standards and methodology have become accepted even by some conservative-labeled scholars, as if they are objectively good standards of the discipline.

The anthology I have in mind at about minute 21 is Do Historical Matters Matter to Faith?

https://www.amazon.com/Historical-Matters-Matter-Faith-Postmodern/dp/1433525712

Craig Blomberg's contribution is titled "A Constructive Traditional Response to New Testament Criticism."