The best way of learning is by mistakes, and if that means learning from others mistakes confessing all IS good as a learning tool, even if not for the soul!
All of our incident investigations and near misses in the organisation are passed around, so everyone can learn lessons from any mistakes made, as well as take home the things that went well.
I can fully understand how and why such an incident can and did happen, and would certainly not pass judgment on your actions, and can only hope others might learn from the events.
Your response by making a PAN PAN, is a very good lesson, and it should be taken a good response. I personally think that getting out of the boat to clear yourself would have been very risky, as even shallow water, and a rising tide, and choppy waters are potentially lethal.
Your best lifeboat is the one you are in (as long as its floating!) and had you slipped, or been dragged away from your boat, there would only have been the occupants of a stranded craft to help you (which would not have been much help!)
With the lifeboat crews on scene, they could do such things, as they practice, train, and have the backup of their other team members to help.
All I can say is thank you for sharing, and giving us a chance to learn from it.
To the critics, I would say do not be so easy to judge, as by criticising the OP, it might discourage others to post similar experiences, and thus deprive us of valuable lessons.