So, it turns out that concrete takes a while to get to full strength. It keeps curing for a long while after being cast, and for best results, you're supposed to keep the concrete damp for several days to give it time to cure most of the way in ideal conditions.
I didn't want to ruin my form, and I needed to make a second mailbox post, so I kept my form damp for a day (wrapped in plastic), then attacked it with a hammer and some determination to get the mailbox post and the form apart.
The only really tricky part was the triangle that forms the inside of the arm. These three critical pieces of wood were a giant pain to make, as they have some really strange angles on them. This meant that I was doing everything I could to get them out without damaging them. One trick I learned was to use masking tape to seal up the concrete-facing gaps between these pieces, preventing cement from flowing into the cracks and locking them into place. With some chiseling and whacking, I eventually got them out mostly undamaged.
The result? We have a mailbox post! It even has some wood grain, although not as much as I would have hoped. The surface has more air bubbles than I'd like, but it still looks okay. This is the first part where I thought this project might actually work out!
But I couldn't admire my work too long - I sprayed it down with water, wrapped it in a thin plastic dropcloth, and left it to cure while I made a second mailbox post. When they were both cast, the second one was wrapped as well, and they were both left damp with water to fully cure for almost a month.