Unlocked + Rooted - how to get from LRX21P to LRX22G? topic

I've been at this for an hour and a half and I can't seem to figure it out. My mom's Nexus 7 is terribly slow on 5.0 and I wanted to get her to 5.0.2 to see if that helps. I have unlocked the bootloader and rooted using NRT, but I cannot figure out how to flash 5.0.2. I have the 5.0 >> 5.0.2 upgrade file AND the 5.0.2 official ROM. I tried flashing in NRT via Launch >> Flash zip and then pointing it to the 13MB update file, but that just kept popping back and from the recovery screen to the TEAMWIN splash screen for 10 minutes before I pulled the plug on that method.

Any help would be much appreciated.

Thanks.