Well, the JL and BA examples are interesting. I had no idea. Of the US-based airlines that fly to Japan, here are the limits: UA, AA: 158cm, DL: 160cm, HA: 157cm. Those are all about 160cm, and likely differ only because the limits are probably natively specified by those airlines in imperial units, and there are rounding differences when converting to metric. But I digress. NH is 158cm. Domestically in the US: WN, AS, B6, NK, F9 are all 158cm. Looking elsewhere, CX, AF, and LH are all 158cm.

So, with the noted exceptions of BA and JL, there seems to be an industry consensus around 158-160cm. I think my generalization is valid: unless your airline has an unusual checked bag limit, the standard checked bag limit (and not the cabin bag limit) of an airline is within the limits of the Shinkansen rules, without having to make a separate reservation for bags. Although there are exceptions to the rule, this generalization will serve people far better than everyone assuming that anything too big for cabin baggage on an airplane needs special handling on the Shinkansen.