What's weird is that we don't get any sense of popularity, and a lot of the names here are not very popular spellings. I suspect popularity would yield pretty different insights, especially if you could see more "sounds like" patterns. For example, my name: Tristan, isn't on the list, but Tristyn is. Tristan is _much_ more common. I found this site that also provides some insight that I think is the same SSA data, th…
I think that in your examples "Austyn" and "Tristyn", the POINT of the "y" replacing "i" is to signal that the name is feminine. Namely, you're having a girl but want to name her Austin, but not have her be assumed to be male. Therefore, roughly 40% of the time you choose Austyn with a "y" (if my calculations from your ratio are right; 85 girls Austyn, 129 girls Austin).
More popular, strongly feminine: http://www.ourbabynamer.com/Sydney-name-popularity.html
Less popular, and used to be very popular male name, now mostly female: http://www.ourbabynamer.com/Sidney-name-popularity.html