I had a similar issue when I bought my first house. It wasn’t pine barrens, but it was a weed farm for sure. It took me two years to completely rid the ground of weeds, leaving my lawn beyond patchy. I took the advice of a friend who is a landscaper. I rented a power seeder. I bought two 75 pound bags of true rye grass from him, which saved me tons of money. I followed his instructions because my ground was very dense. He said to go over the entire lawn with the raking part of the power seeder first. This helps loosen the soil a little. Then water the lawn fairly heavy, wait an hour, then power seed. Spread hay over the entire lawn and wet the lawn well twice. Then water in the morning only for two weeks and do not mow the lawn at all. In a matter of a months time, my lawn looked remarkably better. Not amazing but better. He stopped by and told me to do the same thing in the fall and my lawn would be almost perfect by next spring. He was absolutely right. Using the fertilizer and the natural weed preventer he gave me, my lawn looked country club worthy by the end of the following summer. I kept it that way for nearly a decade before things went sour with my now ex wife. I stopped caring knowing the house was going to go to her in the divorce. But it did work.