Amid(st) lines of communication
Quoting Allen S's answer at the mentioned thread,
Garner’s Modern English Usage characterizes “amid” as implying [purely] position and “among” as implying a mingling. “Amid” and its variant “amidst” are regarded as somewhat quaint, according to that source. Garner prefers the more wordy “in the midst of”, citing its more common usage and its pleasant cadence.
So 'amid/st' is the more clinical, while 'among/st' is more informal, even more intimate. I don't think that's quite warranted here, even if we're talking about the Friendly Islands.
'In the midst of' is apparently more modern-sounding, but I'd still go with 'amid' here. 'In the midst of' has more a connotation of overcrowding, to my mind.
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'Sea lanes' sounds more natural than 'sea lines of communication' to my ears, but I'll try to filter that out.
While 'Islands lie amid important sea lines of communication.' is totally grammatical and uses the more appropriate preposition, there is still something a little jarring to my senses. But I can well imagine 'de-jarring' prior context of varying forms:
But islands are no longer truly isolated....
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Important sea lanes of communication often involve long deviations from great-circle routes....
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There is no a priori reason to rephrase. But perhaps fronting 'sea lanes of communication' (if these are the real focus of the passage) is more appropriate.