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In my grammar (Samson Eitrem: Latinsk grammatikk, 3rd edition, by Bjørg Tosterud and Egil Kraggerud, Aschehoug, 1996), under § 146 Gerundium, he states that:

Akkusativ brukes etter preposisjonene ad og in (sjeldnere etter inter):
Hostis paratus fuit ad pugnandum   Fienden var rede til å kjempe

Accusative is used after the praepositions ad and in (rarely after inter):
Hostis paratus fuit ad pugnandum   The enemy was ready to fight

Nils Sjöstrand (Ny latinsk grammatik, Gleerups förlag, Lund, Malmö, 1960), describes the gerundium as (§ 223) ‘ett verbalsubstantiv med samma betydelse som presens infinitiv aktivum’ (‘a verbal noun with the same meaning as present infinitive active’). He further explains how the verbal noun has no nominative (the infinitive is used), and how the accusative exclusively can be used with a praeposition. For the accusative, he provides the following example (littera c):

paratus ad pugnandum    beredd till att strida (till strid)
inter pugnandum              under striden

paratus ad pugnandum    ready to fight (for battle)
inter pugnandum              during the battle

Again, the only examples given represent ad and inter.

I am trying to express Through surviving you may truly live, and my current attempt is Per superstandum vērō vīvās. Another option would be Superstandō vērō vīvās, using the ablative of means. The latter option, however, does not express the ‘journey through which’ in the same way an accusative can.

Can you use the accusative gerundium with praepositions other than ad, inter and in? And if it is not too much trouble (though it may be that it should be a separate question), would my suggested translation with the accusative work, ɔ: does it represent good Latin?

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I made a corpus search for per near -ndum in Cicero and found no hits for per with an accusative gerund. Without the restriction to Cicero there are too many hits for me to wade through now. I don't recall ever seeing per with a gerund, so I would recommend against it.

There is an idiomatic and common way to say "through doing": It is not *per faciendum but faciendo. The ablative can be used for expressing an instrument, and this use is pretty common with the gerund. You noted the ablative superstando as an option, and I think that is the best one. The use of a preposition like per is idiomatic in some languages but not in others, and *per faciendum sounds to me like a foreign expression forced in to Latin.

In your specific case you can consider using a present participle: Superstans vero vives or something along those lines. The adjective superstes can be used similarly, but the nuance might be off.

If you want to use per to emphasize going through something, then you should go through a noun. Perhaps there is a nice word for "survival" that you could use for through-going? I can't think of a suitable noun for survival, but consider the example of "through living" instead. As noted, *per vivendum is not a good option, but vivendo and per vitam are. The difference between "through living" and "through life" is not enormous. I don't want to discuss the fine details more as it depends so much on the pair of noun and verb. The two verbs may or may not be etymologically related.

There are many words for surviving, and some of them have per- as a prefix. Would that be enough to give the desired tone? Superstare would not be my first choice for surviving anyway as it is more commonly used for more literally standing above. The options that come to mind are pervivere, supergredior, superare, superesse, supervivere.

Out of these options, playing with vivere and pervivere sounds most appealing to me. So how about pervivens profecto vives? Or pervivendo vero vives, as qwertxyz suggests in a comment? There are ample opportunities to play with sounds and repetition of vivere.

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    Very good answer. Also "pervivendo vere vives" (more alliterating, better for a motto) or "superfuturus vere vives", if you want to use supersum at the future participle
    – qwertxyz
    Aug 2 at 12:18
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    @CannedMan Oops, sorry. Indeed gerund equals gerundium, but I was somehow led astray by using the Latin word instead of the English one. The tag is right. // I expanded a little on the noun thing. It's next to impossible to say much in general, as so much depends on the specific words.
    – Joonas Ilmavirta
    Aug 2 at 14:24
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    Do we have any cause to know why accusative gerund doesn’t care for the company of other praepositions than its select few? Or is it one of those linguistic things that just is? In other words: Is the correct question (also) a why, or is it only a how?
    – Canned Man
    Aug 2 at 15:30
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    @CannedMan My impression is that the gerund is a substantivized gerundive. That explains why the former looks like the neuter of the latter and why the usage of the more nouny version might be limited. The line between the two can be blurred pretty badly at times. We might have questions on this very thing somewhere, but I couldn't find one just now. If it seems to be undiscussed, it'd make for a nice new question!
    – Joonas Ilmavirta
    Aug 2 at 15:34
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    @JoonasIlmavirta I agree. I also think that the gerund can be reduced to the gerundive rather than the other way around. If one is interested in this question, a good start is to take a look at this work by Martin Haspelmath (NB: this paper can be read quite easily, I think): publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/… As for your point ("the line between the two can be blurred pretty badly at times"), a well-known case is discussed in latin.stackexchange.com/questions/10809/…
    – Mitomino
    Aug 2 at 17:12

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