Eventually you go back far enough and this breaks down, but we are talking recent history here.
They should be transparent about it and they weren't, and a lot of people here seem to be willing to just trust them and their methodology, but I can't figure out what's scientific or transparent about that. Isn't peer review supposed to catch and correct these types of issues before publication? And if not, shouldn't they be transparent enough in sharing their methodology that the concerns raised by amateur idiots like myself would be easily addressed, or at least accounted for?
Anyway, you have clearly already decided the issue in your own mind and are looking to justify it. So, no I am not going to waste my time providing evidence you can look up if you’re willing to consider the possibility you’re wrong then dare to do it yourself.
You’re effectively complaining they didn’t show their work when using dates from the Roman etc calendar. Historians really care about getting dates correct and have done extensive work to line up each historical calendar where possible.
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.
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.
Isn't the Japanese calendar Lunisolar and borrowed from China? (from the wikipedia link you posted above)