Answered my own question-
Despite the question/answers I'm finding when Googling the issue, CSFR tokens are not necessary when posting to an API.
I went back through and recreated my Eloquent model, the store method in my controller using the Laravel article on the subject (https://laravel.com/docs/master/eloquent#inserting-and-updating-models). My API route posts to the controller@store. My Vue component has a method that uses this.$http.post() to post the data to that API route to create the record.
It should have been more straightforward than what I originally did, but I screwed something up along the way. So, if you're like me and you're stuck on posting data to an API using Laravel/Spark/VueJS, you do not need a hidden field to submit the CSFR- assuming you're posting to a route on the same domain.
This is my experience anyway.
