I am very grateful for all help and input I have got on my bitless-quest.
~C, Mugwump and Sydney all recommended a sidepull, so today I went shopping.
I checked out shops in advance, as western tack is not the most commonly used here, and found a shop 3/4h drive away from home that had one model in stock, and that wasn't too expensive.
It looked all right in size.
It was produced in India, and the leather was a bit dry but not thin, so I bought it.
All my other tack is black (being a dressage nerd obliges!) so a very light brown will definitely not fit in - but the major thing was to get hold of one and try it out.
So I bought it, and once at home I found the leather balm and got to work to get some grease on it.
I also found some padding to the nose band, as I was afraid it would chaff, or be too uncomfortable for her to take a contact on.
So how did it go?
As ~C said, I could hardly feel a difference from the normal snaffle.
I am super duper happy!
Now we can work, and get some sensible work done too.
Today was more of a try-out session, with supplying exercises and a shorter session in the end with some more serious work - but all functioned well; lateral signals, release and contact, both in a supplying, lower and in a higher, more collected form. Fame seemed to relax in it too.
We will probably need some time to fine tune things, but so far it looks very good.
So once again - thanks all for your input!