If you use golden syrup to make biscuits, they come out harder than they would with sugar, they don't come out chewy.
That's why most recipes for ginger nuts include syrup.
Corn syrup would give you the chewy texture you are seeking.
You answered your own question. You didn't cream the butter/sugar properly. And no, don't use
granulated powdered sugar; the sharp edges of sugar crystals actually help to create air pockets in the butter, making the cookie slightly lighter.
Also, golden syrup will make your cookies cook faster be aware of it!
The best way would be to substitute by weight: remove X grams of sugar, replace with X grams of syrup. However...
I think your real problem was with the brown sugar. Older brown sugar can develop lumps in it that don't cream properly, and stay as hard chunks in the finished cookie. I look out for these lumps while creaming the butter, and crush them with the back of a spoon to break them up. If your sugar has a lot of these lumps, you might consider either sifting it before use, or blitzing it in a food processor.