One brand: https://synergeyes.com/consumer/duette/duette-cl/
Or just hard lenses. My first were hard and in retrospect, they were less comfortable, but I had nothing to compare them to so I was more than happy with them. That was quite some time ago, but it was my understanding that hard lenses worked better with astigmatism.
A new doctor said I was on the edge between soft and hard and suggested I trial soft. It felt like wearing nothing. I did sorta notice they would blur on and off at times, but I opted for them and wore them for several years. Then he suggested the hybrid one for one eye and that's what I've been with.
Wherever it was that they wanted to settle (assuming they were ever planning to settle) left everything out of focus.
Eventually I got tired of poking myself in the eye all the time and gave them back.
Edit: Answer here, by the looks of it: https://news.ycombinator.com/item?id=41237519
As a longtime user of toric contacts, I have tried a dozen brands and every single one has the exact same mark. The shape will keep them from moving out of orientation, but it isn't enough to put them back into orientation if put in wrong, at least not quickly.
Care to share exactly what contacts you are using? Do you have astigmatism in one or both eyes? If it is toric and for astigmatism it will say so on the box- many people have it in only one eye, so the boxes will be different, and only one will say toric.
If you really are using toric contacts, but not aligning the mark, I am willing to bet you will be able to find the mark, align it properly, and your vision will be remarkably better.
Edit: One reason you absolutely need the mark is because the optometrist also needs to be able to tell if they are staying in orientation like they're supposed to, by visually checking the alignment mark. It needs to point straight upwards (vertical). If not, they can prescribe you one that is made pre-rotated to compensate.
I have never previously thought about this in terms of rotation (as I was not even aware that the contact lenses were asymmetrical), but I do normally have to blink a few times after inserting the contact lens before I have sharp vision. But in my experience it takes a few seconds for this to happen and does not depend on inserting the lens at any particular orientation.
I have glasses too, so I would notice if the contact lenses were giving me significantly worse vision!
The brand is '1 Day Acuvue Moist for Astigmatism'.
A lot of times your local distributor doesn't carry many of the astigmatic lenses because they can sit on the shelf for a while (it can 100x the available combinations) so they special order. I doubt they're specially manufactured per order for soft lenses.