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i am sorry, but no.
The thing is that if I design it to the thin opening there is when the lid is open, you can't get 2Kg spools on it, because it breaks.
If you take a close look at your top lid however, you can see that you can push it a little forward so you can easily open the lid without removing the holder.

I am sorry, but this is the way it has to be, or you have to cut a little bit of plastic out of your top lid, but I wouldn't recommend that.