Sorry if I missed it earlier, but what bit are you riding her in now? Design, material, etc.
I know that you didn't ask for critique on the picture, but it looks like your elbows are well away from your sides, and your hands a bit high. That can really impact the horse's head carriage.
My advice to you is to check tack fit/adjustment. Poor saddle fit or bit/bridle adjustment problems can be the root of a lot of horse posture problems. Always rule out physical pain first.
Next, reassess your position. I was having similar "softening and rounding" problems, and I took a step back and looked at my own equitation, which was a major part of the problem. I dropped my stirrups a couple of holes, got my elbows back by my hips, and focused on sitting back and deeply instead of tipping forward, and got an instant positive response from my horse.
You shouldn't be pulling on the horse's mouth at all. I see in your profile that you do Parelli. I like a lot of what NH has to offer, Parelli system included, but one of my beefs with NH is the vertical flexion by pulling the face. I teach mine lateral
flexion and the one rein emergency stop, but vertical flexion does not collection make. I leave the vertical stage of the flexion alone, and I'm doing more of a classical dressage line of work for my horse from that point on. True rounding and collection comes from riding from the back end forward. Contact is very necessary, as acceptance of not only the bit but all of the aids. Rein contact should be like holding hands; constant, unchanging, but light. A conversation. Here's a pretty good article: The Art of Classical Riding--On the Bit
If you click on "The Riding School" in the upper left hand side of the navbar at the top, there are tons of other articles that might interest you and be helpful. I especially recommend the articles on classical seat, hands, and Long and Low.
Using a chambon or gogue may be helpful to you, but I've never used one personally, so I can't say much about either except that if you go that route to be sure that you have someone who is experienced working with those tools to help you.