Hi there! I am sorry you are struggling with taming. I am too
so I thought I could tell you a bit about my journey. I brought back home a 11 week male Syrian 2 months ago. He still does not come on my hand and the process of taming him is slow and frustrating, but I try to be relaxed about it. The 1st weeks I tried various forms of out of cage taming and that led nowhere, the poor thing was super stressed and it was just not pleasant at all for either of us. I abandoned this for various weeks, focusing on getting gim used to me in the cage, speaking to him, feeding treats etc. Recently he tried frequently to get out of the cage when the lid is open, climbing on his platform and lifting himself. I used that to get him either in a carrier or a mug and take him to the bathtub. He explores a bit, I’ve put treats there, and he is definitely more relaxed. When he goes into the carrier/mug I take him bacl to his cage, so he knows he can go back whenever he wants. I’m now trying to get him to come on my hand to leave the cage. No luck so far but we’ll see. Basically he is far from being tame but I keep trying and most importantly I enjoy the fact that at last he does not freak out the way he used to. He is more confident and eager to explore and I take that as a good sign.
Finally (sorry this is a looong post), your cage might be on the small side. Many advise no less than a 100x50 enclosure for female Syrians who are notoriously demanding space-wise. Maybe you could upgrade at some point? An Ikea Detolf is always a good option. Good luck and keep us posted!