Thanks again, JWR! I'll try your ideas.
So I have figured out that it's the left brake pedal that is the issue. And I figured out that if I pull back on the lever that normally serves as a parking brake (although it has not been in use during these incidents), it causes the brake pedal to release. I can't see why.
I called my dealership about that, and they were quite interested, but no one has yet indicated that they understand why it is happening that way. They're still thinking about it.
Do you happen to have any ideas on this?