Samsung - Galaxy S III (LTE / International) - i9305 - Documentation Suggestions

I think maybe I am not fully understanding your question. I would call a Stock ROM something that came as close as possible to Samsung official. Samsung official are not actually published, so you have to use an archive; 4 linked here I would recommend.

What is a stock ROM and how do I get one? have downsides of navigation, speed and offers of premium service – so one can see the attraction of this doctored XDA version.

I would not use it for this job.

Perhaps you could explain this in different words in case I am misreading your situation.