Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
Reflash back to the version you had before you flashed 4.3. (Wipe cache, Dalvik cache and do a factory reset first.) Then it should start bothering you to update to the official 4.3.
(Back up EVERYTHING first - you'll lose all your user apps and all your data.)
You can (most likely) find the original ROM at SamMobile Firmwares (enter the model number, not S3). Make sure you get the firmware for your country and/or your carrier. (And don't root the ROM after you flash it - rooted phones can't be updated by the official update.)