I ran a JMeter load test with one hundred simultaneous visitors to see if it is practical to write an array to the wp_options table via the Options API, knowing the array needs to be updated for every visit.
This test confirmed that only a portion of the database updates happened in the way they need to, without overwriting other versions of the array. I expect the exact proportion of failures will vary with load, but since I need my state information to be reliably available, any failures make this a non-starter for me.
My plan going forward is to create a custom table similar to the postmeta table, but tying my unique form ID and unique API ID together rather than a post.