Hi kimchi.
I wouldn't tie the branches to the string. There's usually no need to- except rarely - then I use pipe cleaners to arrange them the way I want- just when tucking doesn't work. Anyway- you're going to need to move those branches more times in the near future.
It's kind of hard to explain what to do, but - if possible - you want to have more growing tips at the screen level. You can accomplish this by moving the longest branches out to the sides of the screen as they get long enough, and by then hopefully any up and coming branches will be long enough to reach the screen closer to the center.
You may have to move the screen up or down to get the branches arranged the way you want.
If you don't have any new shoots coming and are going to end up with only a few budsites- you could always just go for it. You'll have less buds and maybe not be taking full advantage of the scrog thing, but they'll be bigger buds.
When you get the plant flowering it will stretch a bunch, and any existing limbs will get longer. But I wouldn't count on a bunch of new growing tips appearing and making it up to screen level in time.
You're doing fine. It's really not something you can mess up too easily. After you start flowering - and arranging the limbs within the screen- you'll see it becomes very obvious how to proceed.