How to get files off of a kindle fire HDX?

I have a 3rd generation 7" Kindle Fire HDX, the screen is broken and completely unresponsive to any input, and the micro USB port doesn't work unless the cord that's plugged in is angled a specific way. A combination of both these things have stopped me from being able to get some very sentimental files off of the device. I've read the relevant repair guides, but I'm very inexperienced with this sort of thing and I'm afraid of doing something wrong and potentially damaging the device further. Is there an alternate way for me to get what I want?