What makes 江戸 "hist" is that it's not merely an old name; it refers to a particular period in the city's history.

I'm happy with "arch" here.

The difference seems a little subtle to me (江戸 is historical even though it still exists by a different name), but I think I see what you're getting at. I guess this term is maybe too colloquial or unofficial to count as historical.

Saito glosses 秋津島 as "(An archaic name for) Japan". Shinmeikai defines it as "「日本国」の古代の異称". Meikyo tags it as〔古〕. I think "arch" is appropriate.
The "hist" tag indicates that the term refers to something that no longer exists. Only the "Yamato Province" sense of 秋津島 fits that description but I'd argue it's still archaic given that the usual name in contemporary Japanese is 大和国.
I don't have a problem with using rK on this entry.
Probably best to lead with the "Japan" sense.

@@ -27 +27 @@
-<gloss>Yamato Province</gloss>
+<gloss>Japan</gloss>
@@ -32 +32 @@
-<gloss>Japan</gloss>
+<gloss>Yamato Province</gloss>

If the absolute n-gram counts were low for all three forms, I would definitely agree that [rK] wouldn't apply. (Say, 40 counts for 秋津島, 30 counts for 秋津洲, and 0 counts for 蜻蛉洲). At that point, the margin of error is too great for the corpus data to be meaningful.

But that's not the case here, and IMO it's not wise for us to be creating exceptions to rules / guidelines without very good reasons. Best to keep it simple.

Are these senses really archaic, though? They are included in all of the more selective kokugos which usually don't carry as many archaic terms (shinmeikai, meikyo, oukoku, iwakoku). I would've thought that the "historical" tag would be a better fit. The kokugos explicitly state that あきづしま is an "old" reading, which I interpret to mean that あきつしま is "modern," meaning that the term still appears in modern contexts.

@@ -11,0 +12 @@
+<ke_inf>&rK;</ke_inf>