OP, changing the bit and bridle can be essential to your retraining process, so it’s a great question to ask. Many horses who are chronic pullers have numbness or nerve degeneration around their bars and tongue, which is why it’s so easy for them to hang out there. In order to find connection to your horse’s mouth again, you do have to adjust this so that the horse can really feel you. That means changing the action of the bit and where it sits. The gag bit has a lot of poll action (the baucher does not, btw - no leverage) which is why you’ve probably had success, but even a bit that changes the placement of the action (ie more tongue action instead of bar action or vice versa) can help. You’ve said you’ve played with this a lot over the years, so unfortunately you might have used up these options to some degree. However, moving the bit up or down in the bridle may help. Most people have the bit on the high side, so lowering it a hole or two (you can go down to no mouth wrinkles, but just make sure you’re not hitting teeth) may bring it into contact with more sensitive tissue. Even trying something a bit off the wall, like a kineton noseband, will also shape how the bit affects the horse by distributing some of the pressure to the bridle. Bit down in severity, not up, when trying this, because she may have totally different reactions than you’re used to, and you don’t want to ruin this part of her mouth.
CAUTIONS: That said, she’s getting worse and you don’t have many more places to go with this because you’re already in a really harsh bit. So, if you’re not willing to really take the time to step back and lay a new foundation for this horse by re-training her, don’t do it. You’ll just end up souring her to poll pressure and have a back-sore, curling horse. If you want and are ready to make this journey, which may mean adjusting your competition schedule, then you need to go back to the source of the problem - correct fitness and muscle. What people often mistake for laziness in horses usually derives from a physical inability to do what is being asked. Yes, the laziness plays in - that’s why you’ve got a puller and not a rearer - but the problem usually stems from more than “she just won’t go forward or use her hind end.” She probably was not given the time to properly develop these muscles so that she COULD use them, and when her strength gave out, she started to lean on the reins.
If you’ve ever heard a fitness instructor talk about working until you can’t “keep form,” it’s the same for horses. Only they can’t tell us they’re tired, so they modify their body to an incorrect result to try to comply with the request (it’s not like they want to get kicked or swatted). Then they build muscle around the incorrect result (aka pulling) and “it gets worse over time.”
Even if you’re riding her regularly, that doesn’t mean she’s strong enough to carry her own weight and rock back onto her haunches. Just like a runner can’t necessarily do chin-ups, your horse can’t necessarily do dressage just because she’s fit to jump. So, if you want to really solve this, do change the bit, and then spend a couple months building her up from behind. Do it slooooowwwwly - she will only be able to hold herself for a few seconds at first. I would suggest using caveletti once or twice a week to build that muscle and teach her to hold herself. Ingrid Klimke has a DVD set about this so you can do it properly without rushing. You can have a nice, soft rein, and it’s a totally different dynamic than “dressage.” Plus she will only have to work for a short burst before she can rest, and that is how you actually build muscle. Body builders do reps, not just holding up weights, because muscle is built by moving between extension, contraction, and relaxation. Be conscious of this in all that you’re asking her to do, and praise like crazy when she does engage even for a little bit.
Then, in a few months when you have a horse who can actually comply with your request, you can begin to worry about pulling it all together. Don’t even think about the head before that. Best of luck to you!