I believe I read "Our Town" at some point in high-school English class, and I know I saw the play a number of times as I worked in the light booth at the back of the auditorium as it was performed, but I've obviously forgotten quite a bit about it, so it's interesting to revisit it in spite of the frustrations of dealing with the one who is posting the questions....
I'm not sure that I find #3 to be as off-base as #4 does, so I found the 1theory worth checking out. While "fight" is not normally pronounced as "fit" in AE (hint to keeblerelf: there is no one, unified version of AE and BE, just as is true of German in Germany, in Austria, and in Switzerland, etc., although it is fair to say that there is a standard version of each of the above that takes on regional variants ). I've been to many states in the US and appreciate the various ways in which AE is spoken there (some more than others), but I can't say I've encountered every variant, so I can't exclude that pronunciation out of hand.
I know that the OP resists using Google or whatever for assistance for some unexplainable reason, but I find it helpful to do so, even in questions concerning my native language.
Here's something I found about Wilder's use of language:
Wilder comprehended a truth about writing that is very difficult for most student writers to grasp — that is, if you want your writing to have universal impact, you must make it as specific as you can. Thus, Wilder didn't set the play in some nameless Everytown, USA, but in Grover's Corners, NH. He infused it with New England dialect and style. Be sure to point out all of the wonderful New England language quirks that he uses in the play. He makes use of specific regionalisms: "hush-up-with-you," or, my favorite, "'tain't very choice." He spells vernacularly (hull trip for whole trip, git for get, stummick for stomach). He uses euphemisms that add depth and personality to what could be clichés, as when the Stage Manager notes, about the town graveyard, "We're coming up here ourselves when our fit's over."
The author doesn't seem to treat "fit" as an example of Wilder's use of regionalisms etc., but rather a euphemism to avoid a cliché. In this context, the standard phrase is clearly "when our life's over."
In other words, everyone will end up in the cemetery when they die.
Re #2: While "throw a fit" is indeed a phrase that is used, it doesn't apply here.