I haven't used the llama2 models much in quite awhile, because they just aren't very good compared to other options that exist at this point. The instruction-tuned variants of Mistral and Mixtral seem to have very little trouble responding in JSON when I ask for it. However, with LLMs that you run yourself, you can also enforce a grammar for the response if you want to, guaranteeing that it will respond with valid JSON (that matches your schema!) and no extraneous text.
Something potentially helpful here: https://github.com/ggerganov/llama.cpp/discussions/2494
If you fine-tuned a base model (like the one in the article) on various inputs and the expected JSON output for each input, it would probably do even better.