First off I would like to say welcome to the forum and I'm glad to see you are being open and getting help for your horse. As you can see, you will get many different opinions. Don't assume one way is better than others because more agree to it.
So much I want to say in response to others that I don't know where to start.
I will agree that you should stop using the twisted bit and go to a smooth snaffle. Don't throw away the twisted because it does have a place in training, just not an everyday bit.
When you flex your horse from side to side, does her head go above her whithers when she changes sides? If so she's not ready for vertical flexion. Keep flexing side to side until her head stays level, then she's ready for vertical.
Some don't like the one rein stop because they can't get it to work for their horse. It's more than just pulling the rein. You have to be able to disengage their hind end as well. Can a horse still go forward with it's head bent around and looking at it's rear? Yup, been there, done that a few times. Not safe at all. Could I control their rearend? Nope, but that's where their forward motion comes from. Is teaching the one rein stop bad and useless? Nope, anything you can teach your horse to do betters the communication between you two. Another reason the one rein does help is that when pulling both reins, the horse can brace against the bit. Using one rein makes it more difficult.
To Hoofprints in the Sand: Using the side reins may have helped with your horses head carriage, but did you ever think that the time on her also changed her? A horses head position relates to their energy level. When they are excited, alert, nervous or high energy, their head is high. When they are calm and relaxed, they will carry their head low or level. Some breeds do naturally carry their head high but they can also carry it lower naturally.
Many dislike the TomThumb bit. Some don't like it because of the "quality". Some don't like it because of the straight shanks. From what I understand, a curved shank will release quicker, but can produce more pressure than a straight shank. There may or may not be quality flaws in the way it's made, I'm not influenced either way. Just like the twisted bit, it can have a place in training, but I wouldn't discard it completely.
Mls said to lope the horse basically until it wants to stop. This can work with warm blooded breeds but not the hot blooded ones. If I tried that with my wife's horse, he would drop over dead before he would want to stop. He's an Arab cross. Not sure what breed the OP has since she doesn't state it.
Finally my suggestions: I would keep working on flexing her, on the ground and in the saddle. Work on teaching her to give to pressure, and release at her slightest try but there must be a try. When she gets what you are asking, then you can ask for more of a give. Ask her as soft as you can, count to three before increasing the pressure and repeat. For stopping, start at a walk and when you stop, have her back up quite a few steps. I don't use verbal cues, so when I ask to stop, I sit for three strides then ask with the reins.
Some will disagree with what I've said and that's fine. It works for me. It would be good to find a trainer or someone that can give you hands on experience.
On a side note, I follow what Clinton Anderson teaches. However, I've never been compelled to buy any of his products except his videos if they were cheaper. I can get any of his "tools" at a local store cheaper without his name on it. So can everyone else.