What type of trainer are you working with currently? IMO a 'positive only' trainer is not the way to go with this breed.
The leash wrap is more aversive than a prong, I would try a nylon martingale collar or MICRO prong and see how your dog does. Micro prongs usually need to be purchased with extra prongs for bigger dogs.
Definitely. We started out consulting with a "positive only" trainer for a few issues we couldn't work out with Minka. We thought our dog hated us, thought we were doing everything wrong and made a huge mistake adopting her. We felt like doing any kind of punitive measures would break her spirit and make her hate us. This forum has been a wealth of information in general but we had been scared to ask here because every search just turned up "positive only or else you hate your dog/you're doing everything wrong" type responses followed by one or two people piping in to say "Positive only is ideal, but don't be afraid to do what you need to. They're all different" followed by a gang assault on those people by the others.
Some dogs need different things. Minka doesn't care one way or the other about ANY (we've tried it all) food item. It's not a motivator and it doesn't really work as a reward. She just isn't into it. She'll eat if she's hungry but outside that, not bothered. If you withhold food for training sessions, she just won't eat. Not interested. Toys, heh, they're the only things she ISN'T interested in playing with. Not a reward. She doesn't care. Praise is nice, she loves attention, but it doesn't override what she's doing if she is misbehaving. If she was a human, she'd be the type of kid that you can't send to bed without dessert or take away a favorite toy and just needs a good pop on the ass every now and then.
Positive is ideal, but sometimes for some dogs it just doesn't cut it. There are a lot of snobs at the dog clubs and on the internet that will look down on you if it doesn't work for your dog, but who cares. Those who say a dog is a dog is a dog and all methods work the same for all of them don't know what they're talking about. Otherwise Minka would dance for cheese and I'd have been able to get her to stop trying to kill our Chihuahua by offering her all the toys she can't be bothered to play with
She's figured out she'll do what I said when I say it because I said it and I'm the boss and that drawing blood from humans or getting too rough with our other dog results in serious consequences, not just more pleading for her to "pretty please stop it or I'll ignore you while the other dog dies or you shred the **** out of our legs and clothes". Our relationship didn't suffer. She loves to play more now than ever. She is amazingly gentle with our Chihuahua now and they are inseparable. She greets me every time I come home like she hasn't seen me in weeks where before, she was indifferent. She eats better, she walks better, she listens no matter what the distraction. We'd still be fighting on everything if I'd listened to that nonsense in her case. Again, works for some I'm sure, but not for her. She needed (and apparently wanted) an actual authority figure that didn't just toss out pleading and idle/passive "punishments". Now, no punishment is necessary. She's the happiest little thing and we're the happiest puppy parents.
On the topic at hand though...
For her, walking with a flat buckle collar just wouldn't work. She'd pull until she was about to pass out (literally wobbling). If you stopped, changed direction, whatever - she'd just keep doing it. She'd just do it harder if you did those things. Her opposition reflex is insane. It even shocked the local GSD expert we finally located in our area. We went to a Martingale fit snug high on her neck and after a few hard pulls from her, she stopped doing it. She now walks fine. Had she not though, I wouldn't have been afraid to move to a prong collar. Everyone's opinion and experience is valid in their case. It doesn't apply for everyone. Dogs are not all the same, can't be handled the same and don't react the same. Just like people. And just like people, sometimes you have to just do what works before someone gets seriously hurt or before the relationship becomes so strained no one is happy and every interaction is miserable for both sides.