I know it's been 6 months since your post, and since I am new here, and your problem is not marked as "Resolved", I figured I'd respond.....This may help others.
After you d/l the OTA zip, unzip it. The resulting folder should be copied to an SD card (if available), and reinserted into your already powered up TF300T. the system should recognize the card, and find the update during the initial scan of the card. By the way......the unzipped JB folder should be in the "root" of the folder, meaning---not as a subdirectory of another folder. Hope this helps. Good Luck, if still required.