Pailin Chongchitnant has an updated video on homemade rice noodles, and she directly addresses the issue I had when I tried this previously. Here’s my note when I made Pad See Ew with Chicken:

None of them came off the pan easily. I tried non-stick cake pans and a pyrex pie pan, and they all left a starchy film on the bottom. I don’t know if that's from being too thick, undercooking, or what.

Pai notes in the new video (around the 7:04 mark):

Before you peel the noodles off, this is very important, let the noodles cool completely. If you don’t, the noodles won’t release from the pan fully, and then when you peel it you’ll notice gumminess that sticks to the pan, and I figured out that that's because the noodles are still warm when you remove it.

So there’s an explanation for my problem! My noodles were still too warm to peel!