If I’m understanding correctly from some other emails, people are saying the
cheek thickness is increasing due to humidity.

While increased cheek at the escapement thickness could lead to a binding iron,
if the overall piece is experiencing an increase in humidity than the overall
width is going to be growing as well.

Is it possible that the entire body is actually shrinking which would lead to a
binding iron.

The solution remains the same regardless. grinding the iron.

It is my understanding that very old planes are always shrunken in comparison to
their younger selves even when kept at the same humidity.

This (age) is the reason for so many blown cheeks and misaligned profiles,
though of course a move from a higher RH climate to a lower one can exacerbate
the process.

Matthew Groves
Springfield, MO