Just basing the comment on what the article said regarding bitting.
I understand that you’re asking about a thinner version of the Turtle Top, but have you tried the Turtle Tactio? The bit arms are thicker towards the bars and thinner over the tongue. You can see the bit here
and if you scroll down you can see how it lies on the horse’s mouth and tongue as compared to a Turtle Top and to a generic double-jointed mouthpiece with a lozenge.
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I actually took both of these bits on trial at the same time to compare them; she hung more on the Tactio so I opted for the turtle top.
Horses and their opinions! 
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This is why I have a bit fitter coming next month who is not tied to any one brand. Horse was ridden in a french link when I got him but because of the rules I went with the turtle top after meeting with the NS agent here in Ocala. He is still fussy. We will see what the other fitter says.
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I’ve considered doing this in the past - hard to find the service locally for some reason! - but my saddle fitters (through Hastilow) do offer bit fitting services. Since they are in PA, it’s hard to get an appt. within a couple of months - my regular saddle fitter there is heavily pregnant, which makes things more difficult!, but apparently they offer the service remotely as well:
Complete Bit Assessment & Fitting Services
Mouth discomfort is one of the worst kinds of pain and distraction. Horses have a small range of concentration at the best of times, so it is paramount that you chose the correct size, make, model, and design specifically to suit your horse’s mouth anatomy. Poor bit fit, the wrong type of bit for the mouth shape or use and the wrong purpose means your horse will be at the least distracted and at worse in pain.
HCS, USA Saddlery offer not only a Bit Bank called “lease-a-bit” which allows you the ability to trial several bits before you decide what works best for you and your horse, but also offer a complete Bit Fitting and Assessment service. Clients have several options;
- Bit Fitting service as an “in person” visit; scheduled much like a saddle fitting appointment in our saddle fitting service area. A full mouth assessment is written up along with a compete evaluation of all bits currently used, followed but professional fittings and test rides of any of our large stock of Abbey England Bits, Beris Bits, Fager Bits or Neue Schule Bits.
- Bitting Assessment service can also be done through email and phone as a questionnaire along with photos and video of the issues involved. After our staff evaluate we provide educated feedback and suggestions on bits to trial.
- Bit trials offered through HCS,USA Saddlery are through the lease-a-bit program, where you can trial several bits of our recommendation or your choice for 14 days. Then keep what you like and return the ones not suitable for a small fee.
Our Bitting experts are qualified with the NS Academy, the only academic educational qualification in the world. There are three levels to develop both the understanding of the mathematics and physics involved in bitting. In addition to, our experts also participate in ongoing research projects that both confirm and debunk the rules of bitting we have been taught.
HCS, USA Saddlery in addition to professional saddle fitting services, bridle fitting services and bit fitting services also offer sales on new and secondhand saddles, bridles and several brands of bits. We offer test rides and trials on a large range of our brands! Listed below are our current fees for services. Please contact the office at 240-835-5566 or fill details or email at info@hastilowusa.com with questions, photos and current tracings if possible.
I guess the only potential issue is that they only work with four brands. Something to consider, though - and meanwhile I can order a bit to trial from the company recommended by @Jealoushe 
Ok so please hang with me here, I am a former jumper with a huge bit box, switched to dressage.
Given your description of your mare. I would recommend trying a Boucher in your usual mouthpiece. If she likes the stability, that is going to give you the most. I know it USED to be legal USDF and USEA but I am not sure now, as I haven’t had a horse that liked one for quite a few years and they change the rules so often.
It’s interesting that you would say that since I used to use one on her mother! I was considering it – but I’m not sure whether they make a thin enough mouthpiece – and yes it is dressage legal.
I’m afraid she’s going to hang on it is my only concern! Her mother also had a fussy mouth, and liked the stability of the Baucher - but her mother is way more compact and uphill so I didn’t have to deal with the hanging and leaning issue. 
