Scholars put the creation of the Mishna at around 200 CE, and the Beis Hamikdash was destroyed in 70 CE, so you are at the edge of the range where a person who was very young in the Temple era could have as a very old man known Yehuda HaNasi when he was young. And in fact, Maseches Middos is full of the testimony of Rabbi Eliezer Ben Yaakov, who seems to have seen the Beis Hamikdash and whose uncle served as a priest, but who also is recorded many times in the masechta as not remembering the function of various parts of the Temple complex. You very much get the sense of an old Eliezer Ben Yaakov telling stories of the glory of the Temple to his young disciples, and them struggling to fit together the inconsistencies in the old man's tales and imagining this wondrous place they only know as a devastated ruin. It's so heartbreaking.

Does Chanina sgan hakohanim show up?

This "fallibility of memory and also this person didn't actually measure anything" is how I feel about the whole height of the stairs thing.

This might be my favorite mishna. There was a stairway wrapping around the outside if the Heichal. Why? Sometimes the Kodesh Hakadoshim needed maintenance but nobody could go inside, so the workmen would climb to the roof and use hooks to pull things out of the Heichal and to return them after cleaning or repair. I love the mix of awe and practicality at play here. Look, the Kodesh Hakadoshim might be God's resting place among Israel, but it's also a physical place and entropy exists.

I remember stuff about the maintenance problems in Yoma, too. It really brings in that this was a functional space and had functional needs.