Custom Recovery can't mount anything

Alright, so I've got this Nexus 7. The 2013 wi-fi one, running the most up to date stock Marshmallow. Trying to install Cyanogenmod on it. Specifically, The 01-07-16 nightly that corresponds to my device. I thought it would be simple. Reboot into the bootloader, flash twrp, wipe my device, flash cyanogenmod, and then set the device up and be done with it.

That wasn't the case. First, I could not get twrp to flash to recovery for the life of me. I tried 2.8.7.0 and 2.8.6.0. I could get it to flash to boot just fine, but it would not flash to recovery. So I figured I'd try cwm recovery. Still the same issues. Also, I couldn't get anything to mount while I had it flashed to boot, neither in TWRP or CWM.

So I figured I'd take a different route: Go to the official nexus images page found here
https://developers.google.com/android/nexus/images?hl=en
Flash a stock KitKat, install Towelroot to achieve root, use Flashify to flash TWRP, and carry on with flashing TWRP or CWM. I'll admit, probably not the best idea, but I'll admit I'm a bit rusty since I haven't flashed anything in over a year and a half.

I could not get stock KitKat to boot. I tried 4.4, 4.4.2, 4.4.3, and 4.4.4. I just got stuck on the google image that pops up before the boot animation on this device. And yes, both the MD5 and SHA-1 checksums matched up on all of them. I couldn't get into stock recovery either, it just hung on the google logo. Couldn't flash through the bootloader either, same issues as in paragraph two. I could only get it to flash to boot. So eventually, I tried to just return to square one. Downloaded the most recent stock Marshmallow build, and flashed it through the bootloader. Wonderful! Flashed without a problem. Tried to flash TWRP 2.8.7.0, the most recent build for my device (actually if I'm correct, the most recent build in general), and that worked too!

I thought my problems were over. I eagerly rebooted into twrp getting ready to adb sideload cm13.zip but was immediately greeted with the exact same mounting issues I had in paragraph two while twrp and cwm were flashed to boot. So I flashed CWM over TWRP instead. Still the same issues. And I'm about at my wit's end.

Anyone know how to fix this? Also, why can I flash stock Marshmallow, but not stock KitKat? Only thing I can think of is that the files Google provides in the link are corrupt, but I don't know.