As a former brief resident of Kansas, I think the plural of Kansas would be “Kansases”. I may have even heard that term before.
“Arkansas” of course is pronounced differently (the last “s” is silent) so I’m tempted to pronounce it like “Arkansaws”. But I’m not sure how that would be written. Maybe it’s spelled “Arkansases” but pronounced “Arkansaws”?
Irrelevant to the question in the OP. First, you’re talking about a plural rather than a plural possessive. “Deer” is unusual in having the plural the same as the singular. The plural just takes apostrophe "s’ like most other plural nouns: “the deer’s tracks” can refer to the tracks of a single deer or a herd of deer.
I think it can be argued that “Arkansas” is already plural, therefore trying to make it more plural by forming “Arkansases” is pushing it, especially with the silent ‘s’. (Then again we have: one people, two peoples. So maybe the plural should be spelled the same (Arkansas) but with the s voiced. One Arkansaw, two Arkansaws.)
The possessive of the singular should then clearly(?) be Arkansas’s; in the plural I would probably write it the same (cf Jones’s, Moses’s), but you should refer to your official style guide for that case.
Given that only one of the four ships was named Arkansas, it seems wrong to refer to collectively by that name. Instead you would call them the Arkansas-class monitors, and then perhaps just the monitors.
No it isn’t, by any stretch of the imagination. Although the name of the state is derived from a French plural, it is treated as a singular noun in English. Would you say “Arkansas is a US state” or “Arkansas are a US state”? Similarly for the name of a kind of ship derived from the state.
Sure, but he’s probably better off rewriting/writing the sentences to not even have to do that- any way you try and pluralize “Arkansas” is liable to look awkward.
So rather than “The Akransas’ engines were…” rewrite it like:
“The engines of the *Arkansas *class were…”
Or something similar- avoid having to pluralize it by writing the sentence differently.