You seem to be making some weird assumptions?
Here's how I would do this:
Use some LLM, the weights need to be know to both parties in the communication.
Producing text with the LLM means repeatedly feeding the LLM with the text-so-far to produce a probability distribution for the next token. You then use a random number generator to pick a token from that distribution.
If you want to turn this into steganography, you first take your cleartext and encrypt it with any old encryption system. The resulting bistream should be random-looking, if your encryption ain't broken. Now you take the LLM-mechanism I described above, but instead of sampling via a random number generator, you use your ciphertext as the source of entropy. (You need to use something like arithmetic coding to convert between your uniformly random-looking bitstream and the heavily weighted choices you make to sample your LLM. See https://en.wikipedia.org/wiki/Arithmetic_coding)
Almost any temperature will work, as long as it is known to both sender and receiver. (The 'temperature' parameter can be used to change the distribution, but it's still effectively a probability distribution at the end. And that's all that's required.)