How old is your doggie?
We have a 9 month old, highly excitable, but highly trainable Labradoodle and she too is a "Puller". Like yours, she has good days and difficult days. We go to puppy training a few times a month and these have been amazing.
It has really been a lesson in patience for me. Walking used to be her suddenly stopping and then bolting forward and I really had to keep my patience in check.
The trainer made the recommendation to simply stop when she pulls, say "No" and stop. When the leash goes slack, we walk. This is ongoing and like you there are days when she'll just do it like a pro, and days when she's just deaf.
When I go out for a walk and we walk at least 4-5k a day, 4-5 times a week, the first part of the walk it critical. So I start technical training straight away. What works for me is the choice of treats; not all treats are equal. I use these tubes of paste that you squeeze out, she loves these and we call it Obedience Crack. She'll do anything for the stuff.
I keep on my my left, hold the leash in my right and at the side of my thigh, squeeze out the Obedience Crack while walking. She sticks to my leg as we walk. Then I give her the command to heel and she sits. I tell her to wait and walk a few meters forward, when she reaches me she heels, I tell her to wait as I walk forward and then call her, we walk and she sticks to me while sucking on the Obedience Crack tube.
Once I reach open field, I made her sit and I take off the leash, tell her to wait and after a minute she can go and get her Zoomies in. This is just how it is.
What I have observed is that I train and train and train something, and feel like it's just never going in and she's never going to get it and then one day, BOOM, she just does it, she suddenly integrates it.
Toilet runs are a trip around the block. At around the halfway mark I let her off leash (not always) and she does her business. Then we walk on leash and I pick up the pace, when I do this she tends to focus and trot alongside me. This helps and when she does this I heap praise upon her.
I've also learned that If I just start praising her, she starts looking for good behavior to fit the praise. So I just praise her all the time and she reacts appropriately.
Good luck and all, I hope that you all settle and have a fun time.