My Nexus 10 won't boot, so I need to copy a ROM from my computer to the device. Since it won't boot, I need to copy it via recovery. I can flash recoveries as needed and install software on my computer as needed, but I need to get the ROM on there!
Use ADB on a computer while your device is in recovery. To copy a file from the computer via usb, use this:
adb push /path/to/local/ROM.zip /sdcard/
This will copy the local file to the device in the specified location. Directories can be created on the device via the shell:
and using the usual shell commands to navigate around and create directories. This beginners guide may also help you.
You might also consider getting a USB OTG adapter. This way you'd be able to put the files you need on a USB drive, plug it into your N10, and flash the files you need. I do it this way on my N7 with TWRP all the time so that I can erase everything on it without worrying.
Have you tried Wugfresh's Nexus Root Toolkit? It should be able to do that.