Hair dryer might desicate your leather and make it somewhat brittle. I wouldn't try it. As I said before, sometimes you use the pliers to push from behind to get the needle part way through then you grab and pull. Also, as stated circular needles are @$%&*÷!# to use on leather. You have to have the tip at 90 degrees to the hole or your poking into leather, not the opening (hole).
Are you using the awl as I suggested to loosen each hole before you take a stitch? That's the best suggestion I've got for you.
As for repair price being roughly equivalent to the purchase price I'm not at all surprised. You can't remove the cushions. This is going to be a pain in several body parts for anyone to repair.
No matter how you repair this, new holes, old holes, it's going to have a different look. Unless you duplicate the thread and method of construction it'll be different. Unless you take apart the entire seam and restitch the whole thing it's going to look "repaired" or "mended". It just will. And it's not going to match the other seams which may or may not bug you.
I'd be inclined to fix it as best I could. That might be buying a remnant of upholstery leather that either blends or makes a pleasing contrast and gluing a patch on with barge cement. You could add more patches glued on elsewhere to make it a design feature. Then I'd find a quilt or throw that worked well with the sofa and have that tossed over the offending seam.
Have you disowned the kiddo yet?