Need to copy files off of Nexus 9 that can only boot into Recovery Mode

[AC Question]

An update a couple days ago broke my Nexus 9. Now when I start it, I get a message about the tablet being corrupt, and then it tries to boot but just gives a picture of a little dead Droid guy with the phrase "No Command" under it. I don't need help with that specifically, I assume I'll need to do a factory reset or send it into HTC. Problem is both of these options result in a wiped drive, and I have a bunch of AK Notepad files I need to pull off of here before that happens.

I can boot into Recovery Mode. A Google search tells me that some Droids have a backup option here, but I do not. Is there any way to do this without rooting?