In reply to:

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The disks are mounted read-only, and there's not enough space in persistent storage to keep VBR headers for (potentially) every track on the player.

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I assumed there'd be space wherever the seek maps go...

It might be sufficient to store a mark for each track that needs attention, and an ability to fix them at sync time (possibly not by default, though, as it would be time-consuming....)
Fixing the total time is more important than the VBR headers, though.