Why would you feel anger, rejection or betrayal because your dog went into hunt mode? Your dog isn't doing anything to try to make you feel this way....it's simply being a dog.
I agree with the obedience training, partly because it will help you to understand your dog's psychology.
I think you have learned that letting your dog obsess for hours in a no win situation isn't helpful. You conducted an experiment and the results tell you not to do that again. Sounds as though taking the dog away from the frustrating situation early is a better strategy.
I'm a bit concerned about the second strategy...treats etc when dog has behaved in a normal beagle way that is undesirable in its environment....because I think you are likely to condition your dog to associate the inappropriate (in the situation the dog lives in) behaviour with rewards.
I'd be doing something calm and assertive to let your dog know that you don't approve and the behaviour won't be tolerated.....eg moving your dog away from the situation without any positive social interaction.
One of my cats had got himself into his pure cat mode the other day....he was frustrated because he couldn't get to another cat that was in his territory. His interaction with his human mode was switched off. I had to bring him inside, so I had to grab him and he bit me. I wasn't upset....he hadn't betrayed me or anything, he was intensely upset and frustrated. I just picked him up and brought him inside.
Big difference....he's harmless. Yes, he can bite me, but unless he's utterly panicked he won't hurt me. If he's so upset that he might really hurt me, I can pick him up in a way that won't allow that to happen. He's a little cat. I can manage him.
You have a dog which could really hurt you. There's no need to feel bad, but you do need assistance to assess the risk and support you in fixing the problem.
Listen to the dog folk and get to a dog trainer if I were you.