I use a Thalia. When I got it, it worked just a little bit better than my G7th.
For those who are unaware of Thalia capos, they offer different radius pads for different guitar brands. My Martin uses a 16" pad. Thalia is aware of the problem and has been working with some of us 12 string users and first, they added an extra high pad kit. I was sent one of these and it vastly improved performance but I still needed to squeeze the capo to assist the tension for a clean tone.
This info led to a heavier spring capo. When I received the capo with the heavier spring, I found I had the perfect 12 string capo.
Like some of the others who have responded to this thread, I do not capo a lot, choosing to just play in a different key but there are some songs that need a certain chord, etc.
Because of the correct radius for the specific guitar, increasing the tension does not cause the guitar to sharpen up like other capos do.
I urge anyone who uses a capo on his 12 string to try it but specify 12 string when you order. They are really on to something.
I realize, everyone has their favorite capo and I have owned most every brand for my 12 string over the years. I could always make them work but, it took a lot if fiddling. I set the Thalia and forget it. It is so easy. They are not cheap but they are worth it. I have 2 and I paid full pop for them. I'm not affiliated in any way.
Martin 0-18t tenor guitar/MyaMoe baritone ukulele
Kamaka HF-4 baritone/Outdoor tenor ukulele
Kay El Bee baritone ukulele
Vega Little wonder tenor banjo