I'm unfortunately quite familiar with embarrassing parents that refuse to stop partaking in a certain behavior or conversational tactic no matter how much you ask. In my case, my father would almost always insist on flirting with waitresses at restaurants we went to, even though he is significantly older than them and even when my mother is present.
It was annoying, awkward, and seems to check a lot of similar boxes to your situation, so hopefully my advice will be useful to you.
TL;DR: Leave the situation.
You can't control him, not really. From what I can tell from your question, you've tried to talk to him about it with no success. If he doesn't choose to control himself, the only thing you can control in the situation is yourself. Once he finishes his usual spiel, give a polite smile to the other conversation partner, apologize on behalf of your father, and then walk away. It's critical here that you don't seem angry, only disappointed.
Here's a fairly extreme example, for when a waiter is talking to you at a restaurant.
Waiter: Hello gentlemen, how are you doing tonight?
Father: You know, my son makes XYZ etc etc.
You: Polite smile, shake head I'm so sorry about my father, please excuse me.
Then calmly stand up and walk away. Your father will inevitably come to follow you, or if he's stubborn perhaps you will simply need to browse your phone for a few minutes before returning to the table.
By taking this stance, you are controlling the situation and removing yourself from a frustrating situation. You've shut down the conversation entirely. Your father will likely ask why, but thankfully you can be honest and explain that you didn't want to be in that situation since it was so awkward and uncomfortable, and so you thought it would be best to leave for a moment.
Ideally, your father will get the gist, realize you've taken control of the situation, and decide to moderate his behavior.
If not, you can at least control how long his nonsense continues.
Either way, I hope it helps. Choosing when to leave is also a form of boundary-setting, and hopefully you can set healthy boundaries that your father will understand are acceptable.