But in the monty hall, the "discloser" is limited by my choice/observation. It is literally part of the framing. In this framing, there is no limit based on my choice.

Consider, if you tell me that the Smiths have at least 1 girl, and I meet their daughter but you haven't met either, I have no way of knowing if I met the 1 girl or not. I could ask you, but you would just say, "I don't know, could be her. Could be the other kid. I just know they have at least 1 girl."

This is very different from the monty hall case, where the announcer knows what is behind all doors.

Similar. But different. I was using coins as an example elsewhere. If I flip a dime and a quarter, and tell you that one of them is heads, do you have increased chance of knowing if either particular one is heads? This is more liar's dice than it is monty hall.

I have no idea what point you're trying to make. I am aware the selection process is different. If you understand the argument now but you're just splitting hairs about whether it's similar to Monty Hall, fine let's agree to disagree. If you don't understand the argument and are trying to use the dissimilarity to Monty Hall as a counterargument then I don't think I can help you any further.

This is not coherent as written:

  If I flip a dime and a quarter, and tell you that one of them is heads, do you have increased chance of knowing if either particular one is heads? This is more liar's dice than it is monty hall.