First off, 'nakya' actually appears on its own without 'rare' earlier in this very song, in verse 3:
Second, 'shinjirarenai ga' in that position would actually not translate to what you intended. As it is, 'ga' would be parsed as the conjunction "but", so it would actually mean something like "I can't believe it, but [...]". To get what you intended, it would need to be something like 'shinjirarenai no wa' (though that has its own set of issues).
Also, you might already be aware of this, but just in case, keep in mind that 'shinjirarenai' is distinct from 'shinjinai' - "can't", rather than "won't" (sometimes you can translate it either way, but it can cause problems in other cases).
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To go into more detail on the contraction itself, the actual transformation is 'nakereba' → 'nakya'. 'nakereba ikenai' is often implied, being (probably) the most common use, but I find it more helpful to remember where the actual syllables come from, as this contraction can also go in the middle of a sentence anywhere 'nakereba' would.
Examples:
-
shiranakya ii koto - things we don't need to know
-
jibun wo aisanakya hito mo aisenai - You gotta love yourself before you can love someone else
I mention this because I believe this is how the two lines in this song should be interpreted.
Romaji: Sugu tachiagaranakya CHANSU wa nigete yuku wakatteru sa
Current: I've gotta stand right back up, I know my chance will run away
Suggestion: I've gotta stand right back up
or else my chance will run away, I know
Romaji: Shinjirarenakya mabataki shiteru setsuna ni kieru yo
Current: We've gotta believe, disappear into the twinkling instant
Suggestion:
If we can't believe, we'll disappear into the twinkling moment
This could be the source of confusion.
(Aside: notice that I've joined a few pairs of lines together. This is because our most reliable source,
kasi-time, doesn't have the lines split like that. While not absolute, this can be useful information for deciphering songs, since line divisions sometimes suggest sentence divisions.)
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