Da gibt es doch eine Redewedung "to thow a fit"? Heute würde man sagen: ausflippen/ausrasten

Throw a fit - Idioms by The Free Dictionary

throw a fit. To become very or unreasonably angry or upset; to have an outburst of rage, frustration, or ill temper. My mom's going to throw a fit when she sees what happened to the car! I was so embarrassed when Danny started throwing a fit in the grocery store.

In the meantime it dawned on me that it could be fight instead - when our fight is over. But I'm not sure.

It would be interesting how it is pronounced in spoken American English here.

 it could be fight instead

Why? And what do you mean by "pronounced in AE"? fit is never pronounced fight.

I was thinking along the lines of fit of grief (i.e. the period of intense grief)? Still an odd way of putting it though.

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.

Oh, an interesting one. Perhaps an old-fashioned turn of phrase, if even the US English speakers find it odd.

I agree that it seems to be about mortality.

We use "fit" to mean a brief period of human activity, as in a fit of rage or remorse - and the OED says that in the past it was used to mean a spell (brief period) of something, as in a "fit of good weather". Perhaps that's the idea. Our life as a brief period of activity.

The etymological connection to "fight" (if there is one) is very old, from Old English (pre-12th century).

FWIW, die Definitionen zu den Substantiven aus dem etymonline-Link in #8 :

 fit (n.1)

1680s, "process of fitting," from fit (v.). From 1823 as "the fitting of one thing to another;" 1831 as "the way something fits."

 fit (n.2)

"paroxysm, sudden attack" (as of anger), 1540s, probably via Middle English sense of "painful, exciting experience" (early 14c.), from Old English fitt "conflict, struggle," which is of uncertain origin, with no clear cognates outside English. Perhaps ultimately cognate with fit (adj.) on notion of "to meet." Meaning "sudden impulse toward activity or effort" is from 1580s. Phrase by fits and starts first attested 1610s (by fits is from 1580s).

 ... fit (n.3)

part of a poem, Old English fitt, of unknown origin; perhaps related to fit (n.2). ...

I also give some credence to the possibility (#3) that "fit" is local dialect for "fight". Although I've never heard that usage, it might be rural or local or outmoded, or all three. Evidence in favor of the possibility is the African-American spiritual "Joshua fit the Battle of Jericho", although in that case, "fit" is dialect for "fought".

m-w.com has this:

fit

6 of 6

dialectal past tense and past participle of FIGHT

https://www.merriam-webster.com/dictionary/fit