Hello, I'm having a similar problem. I was going to install the iOS 17 Developer beta directly from the iPhone, but the "Beta Updates" option does not appear for me (under Automatic Updates). I have developer mode turned on, so this option should appear, but it doesn't. The iPhone is on the latest iOS 16.5 version, and an iPhone 13 Pro. I don't even have the option to download the public beta iOS updates.
Because of this, before seeing this post, I tried the method of installing the beta through the ipsw file and restore feature in Finder. I had the same errors as @obsessive.
Is there something else I could try to do to download the developer beta?