The Haltis and Gentle Leaders are great, but dogs do not love and adore them. That doesn't mean they shouldn't have them. It takes patience to get a dog used to one. I use one with my pup; if she could speak English about it, her words would not be nice ones. But it doesn't really hurt her to wear it and she likes to go out and about so much that sometimes she forgets she has it on.
It sounds as if you're basically doing well with your beagle, and that's great, because beagles aren't always easy to train.
I think you might be wise to take her to some obedience classes at your local pet store, reputable dog training place, or kennel. What's happening is akin to excitable greetings; she's so happy about taking you for a walk she does all the excited, inappropriate things. It's a habit with her; she thinks the noise and furor are acceptable ways of acting in this circumstance.
If I were going to work on it, I would be prepared to take a lot of time. It can't be done in a day or even a week. I would start by calling her to me and having her sit in front of me. I would reward her with a tiny bit of treat - just a taste - when she does this. When she's confident about doing this, I would show her the leash, say, "Good sit," and reward her when she could keep sitting. Even if she can sit for only two seconds once she sees the leash, reward her. Extend the time to thirty seconds or so.
When she can do that, I would practice snapping the leash on her and reward her when she keeps sitting. Teach her a command, like "Let's go," that will tell her to start moving on your command, and reward her for that. (You're using very tiny rewards, right? Otherwise she's getting pudgy about this time.)
You have to practice her walking behavior outdoors in many different places. Dogs are very practical; if you always practice in the back yard, and then take her into the front yard, she'll think, "Oh, I'm not in the back yard, so I don't have to do that stuff!" This reminds me of some children I know, but let's not go there.
If you can get her to sit on leash - preferably beside you, but don't be too picky at first - then reward her. Then walk her just a little way, but make sure she knows you have that bit of kibble or carrot or dog biscuit in your hand, and reward her every few feet. If you have your hand with the treat near her nose, she's likely to keep her nose (and the rest of her) in the place beside you where you want her to walk.
Don't make her practice too long at at time, but do it once or twice a day. Be very consistent and pleasant. Use a regular tone of voice.
The idea is to make Bessie Beagle think, "Oh, if I change what I do, I have a good chance of training my mama to reward me whenever I sit for my leash or walk next to her." Eventually you'll be able to drop the many food rewards and just use praise, because she'll have the new habits down pat.
I think training a dog is like working with a two-year-old child, no matter how old the dog is. It does take that kind of patience and perseverance.
(If you want to keep trying the Halti/Gentle Leader, take it and Bessie B. to a pet store and ask the expert to adjust it to fit your dog's nose correctly. It needs to be snug enough to work, and loose enough to be comfortable. I don't always find it easy to get the exact fit. Once I get it there, however, my dog is so much easier to work with; I'm guiding her by her head instead of pulling her by her neck.)
Hope this helps.