As I understand it, the swaddling trick is used in medical settings at times.
If you're not up for doing that yet...
It might be worth trying taking the pressure off for a few days. Will she accept a toothbrush against her lips, just pressure not brushing her lips obviously?
I wonder if you can de-sensitise her to it by gradually reintroducing and repeating it initially by not trying to force it inside her mouth but just the brush approaching her mouth, touching her lips, pausing and then being removed... Until she can tolerate that happening without becoming distressed and she starts to relax.
Maybe at first just have the toothbrush in your hand while you're cuddling her or doing other things with her without even trying to touch her with it, it's just something you happen to be holding. No big deal.
Once she's calmer with that start allowing it to briefly touch her in a casual, "accidental" and brief way as if you don't even notice you're doing it while you're doing something else.
You want to make it feel calm and safe and nothing like those experiences with the syringe where she was forced to accept it.
I'd expect her to tense up and react at first but then start to relax when she learns nothing bad happens if she accepts the brush. It will take repetition to achieve that because things that haven't felt safe stick with us for longer than experiences of safety. Progress it only once she's visibly calm about the previous step.
Then step up from there to getting her to accept opening her mouth, relaxing, and then the brush being removed without being used... Etc. She needs to learn that you putting things in her mouth doesn't always mean something nasty will follow, so hopefully the experience of the brush just resting in her mouth and being removed would help step towards that. Rather than the first time she opens her mouth you immediately start brushing her teeth.
When you do get as far as brushing, only do it briefly at first and gradually increase what you're doing.
You would need to be calm and relaxed in your body language and tone of voice too. Casual, the brush isn't a big deal and nor is her reaction. She'll pick up on your anxiety or frustration.
If that doesn't work you might have to step up to swaddling and let her relearn that way, but I understand your discomfort and reluctance. I'd want to try habituation first as I'd be worried about reinforcing the idea that having anything in her mouth will be distressing.
It's not an emergency right now for you to be able to brush her teeth so take that pressure away, be creative and see if you can make it feel safe for her again by gradually reintroducing it.