This is the paper. It did describe the challenges of inferring the full-bloom date from old literary work. But the calendar conversion is not one of the challenges.
By everything I've read, it should be included as a challenge, and they should be explicit about the method they used to determine the Gregorian dates, because it's not straightforward, nor is there even an agreed-upon method or table to use for conversion, yet their whole claim rests on the verifiability of the dates.
This is a list of material and conversion tables composed by the National Diet Library on the old calendars. There are clearly well-established method and researches about this. This would be the most basic problem for anyone studying history in Japan. It may be not straightforward (for you), but it certainly would be too generic and elementary for other historians to read in a paper like this.
If this is what they used, why didn't they say that? I'm not making a claim about what method they used. I'm saying that whatever method they used is prone to error and should be included in the methodology of the paper. What is wrong with being transparent about their methodology? And what is wrong with expecting that level of transparency in a scientific paper making a specific claim?
I have to admit, the passive-aggressive ad hominem attacks caught me by surprise, but my request for transparency with regard to the methodology they employed when converting their dates stands.