Like some I was frustrated with not getting the 4.4 update on my new 2013 Nexus 7. I did some searching and it looked like the manual ADB method was the only one I could find that was tried and true. I did come across a method that walked through updating with the OTA file but I ran into a problem with the recovery not having the apply from SD card option. It then hit me to try the good ole Wugs Nexus Toolkit that I have used with very good results on my Galaxy Nexus. So I downloaded the OTA file from here and renamed it update.zp. I then got my Wugs Toolkit updated and the correct drivers installed. I then launched the Advanced Utilities and selected the Sideload Update option, couple minutes later I had 4.4 on the tablet.
Im not sure if this will help but since I did not see anything like this online I figured I would post it.
Im not sure if this will help but since I did not see anything like this online I figured I would post it.