I don't recall Jaynes discussing it much. Anyone?

For him, I think the reference class is always the context of your problem. Use all information available.

A brief google for "jaynes reference class" turned up his paper on The Well Posed Problem.

http://bayes.wustl.edu/etj/articles/well.pdf

He analyzes the Bertrand Paradox, and finds that in the real world, the mathematical "paradox" is resolved by identifying the transformation group (and thereby prior) that in reality is applicable.

My take on this is that "non-informative priors" and "principle of indifference" are huge misnomers. Priors are assertions of information, of transformation groups or equivalence classes believed appropriate to the problem. If your prior is "gee I don't know and don't care", then you're just making shit up.