It would be great to stop this bad habit but you're worried about jerking on the leash and hurting his back. Mind you, pulling so hard on the leash such that his front paws leave the ground isn't good for his back either.
Part of the problem is that he's so keen to get to the park, he becomes deaf to calls of "heel" and now it's you that's nearly at the end of your tether.
Unfortunately, what sounds like a simple task is deceptively difficult given that Dachshunds love to get ahead, which then involves them pulling badly. Not only is this bad manners, but it's bad for the Dachshund's long low back, as it puts it under strain.
Start training in a quiet place with few distractions, and as he gets the hang of the task, move outdoors. Practice plenty and in different locations, so that he understands he's expected to walk nicely on the leash no matter where he is.
Because of the Dachshund's delicate back, it's better to train him using a harness rather than a collar. The harness spreads the force over his chest, rather than concentrating it on his neck, should he pull.