I have the same problem. Last year I had to put up all these nets. This year I was going to try to plant so many that it wouldn't matter, but for whatever reasons, I only have one. They haven't 'seen' it yet. Maybe I should stop attracting them with the nyger seeds like I usually do. It is so frustrating!!!

From an earlier post of mine today:

The leaves are rich in minerals such as calcium, and some leaves are also collected for nest building. Here in the east, Goldfinches are also late breeders and have their own unique behaviors.

There are several other flowering plants whose leaves Lesser Goldfinches prefer. You might plant those in the same flower-bed to minimize the damage to the sunflower plants.

Do you know of the top of your head the other kinds of flowering plants they like to munch on?

I haven't seen a lot of the little buggers lately (I was thinking maybe they were nesting already), but the last 2 days I'm seeing them again. Thinking of not refilling the nyjer sock when it is gone.