That sounds good news that he isn't biting now. Syrian's usually only bit if they are scared or in pain, but I guess there are exceptions
Good that your training has worked. Does he still try to bite if you pick him up? Because it could mean he has some pain somewhere. So keep an eye on him for that and check his cage set up for any fall risks (I'm sure it's fine, but they shouldn't be able to fall more than 30cm and then only onto a soft landing, such as substrate
Sorry if you know this already. Also he might not be very tame yet. Our Syrian was quite aggressive and wild when we first got him! From a pet shop. He would run at you if you put your hand in the cage. He never bit but threatened to a few times! If we tried to pick him up or touch him he'd leap 2 feet in the air and risked hurting himself, so I came on here and followed taming advice, and we tamed him in the dry bathtub, where he couldn't escape from and couldn't hurt himself if he jumped. It took a few weeks, and sometimes our little boy would get in the bathtub with him and Charlie would run all over him, seeing him as part of the furniture, so he got used to his scent. Mostly we'd put him in there with some toys and let him play a bit and eventually we were able to stroke his back with one finger - he went as if to bite at first, but didn't. The next time he accepted it without jerking his head round and after that things moved on quite quickly and we were able to start holding him a bit, initially by cupping a hand under his tummy while he was in the bath, and just lifting him a centimetre or two but not trying to hold on to him, and letting him just walk off the hand again. We did this a few times and were then able to pick him up and he was tame as anything. You could hold him, pop him in your pocket, stroke him - he was lovely! It was all building trust and confidence. And he stayed tame.
So another thing you might want to try now is the tissue trick. You put some sheets of toilet paper up your sleeve and leave them there for a few hours. Then tear the sheets into strips and put a pile of the paper strips somewhere in his cage, and he will pouch some and take it for his nest. This way he gets used to your scent and won't be so scared of you.
I have to say another reason our hamster was so aggressive when we first had him was that his cage was too small and not very suitable (he was in a rotostak and the units were very small and not well ventilated, plus access was from the top which they can find threatening). I only realised it wasn't suitable when he got stuck in a tube! And then found out more about the best cage size for a hamster and we moved him to a larger 80cm x 50cm cage after finding RSPCA recommended sizes. He was very nervy in it for about 10 days but after that he was happy as larry
A totally different hamster and showing all kinds of interesting behaviour.
So there are many reasons why he might be bitey. It's good you've found a way to deter him from biting but it might be good to look at why he might be behaving like this as well. They can be really scared when they're just babies!
I can definitely recommend bathtub taming for getting used to handling him. I did a short video on it recently. It's not the greatest quality and doesn't show that much but has a few tips
Welcome to you and Freddy and if you have any concerns, come on here and ask, people are friendly and there are some experts and breeders on here who can answer any issues you might have. It would be nice to handle him without wearing the gloves. Bar chewing is usually a sign of stress and sometimes caused by the cage being a bit small as well. Not sure what cage you have, but often pet shops sell cages that are too small.
Blowing on their face can be a deterrant but might not help them feel safe with you.
Here's the video
https://www.youtube.com/watch?v=kjyEme2xcq4