This has been a constant problem with her, ever since she was small. It hasn't improved, and has only become more annoying since she is now 65lbs and very strong.
This tells me that you haven't approached "going for a walk" the same way you've approached training her to compete in obedience in her classes. It's not going to get better by itself - as you said it's getting worse now that she's big and strong and can pull even harder. Prior to Halo I never had a dog that walked all that well on leash because we always drove our dogs to an off leash park for play and exercise rather than doing leash walks. Keefer is now good on leash, (he's 5-1/2), but it was tough for awhile because I had failed to put the work in when he was still young and small enough that it would have been easy. But if I can teach HIM, you can teach HER! Since he was already a full grown 80 pound dog by the time I started, I did use a prong collar on him so I could control him if he lunged, and you might need to do that too. Prior to that, I'd never even owned a prong collar.
Now with Halo, I was bound and determined to teach her to walk nicely on leash from the very beginning. I recognized the mistake I'd made with Keef, and I was not going to repeat it. It took a lot of time, patience, and persistence, but she walks beautifully on leash, and it's a joy to take her for nice long walks. But in order to do that I had to completely abandon the idea of "going for a walk" in favor of training proper leash skills. That meant that some days we spent 20 minutes walking back and forth over the same ground over and over and over and over..... Very frustrating, but she soon learned that pulling did not get her where she wanted to go, and in fact, she often got even FURTHER AWAY!
I think you're right, that she does recognize class as "training" and walks are "not training", so you need to turn that around. Halo is very good at recognizing training too, we've been working with an excellent private trainer (business partner of Michael Ellis), and she made that comment about Halo the first time she saw her. So I made every
walk a training walk.
For example, I went to an obedience fun match the other day, and it was like she had ADD. She kept pulling and I had to drag her into the ring. She worked fine once in the ring, but was bouncing around like a psycho after and dragged me out when we were done. The second time we went in she decided that I didn't exist anymore and actually RAN OUT of the ring.
How about taking her to a fun match and not going in the ring at all? Use it as a training opportunity by working with her in that highly arousing environment, at whatever distance from the fun that you can continue to engage her.