In the Tyrolia line there is the LD-12 (LD stands for Light Diagonal) and Mojo 11 and maybe some others. Both are lightweight bindings. The LD-12 can be purchased with wide brakes. On the Mojo 11, I believe that wide brakes are standard. Both are designed to be mounted directly on the ski and neither comes with a plate.
Two Fischer bindings using Tyrolia technology that also come with wide brakes, no plates and higher DIN settings are the Fischer X-17 (DIN 17) and Fischer X-14 (DIN 14).
I've been skiing in Tyrolia bindings or their Fischer versions for years both with plates and without and never had a problem.
Once mounted, they can all be adjusted to slide back and forth to some extent at the heel without remounting. I've moved mine from accommodating a 311mm sole to a 301mm sole and I know that they can be adjusted further. I'm thinking they have a total range of about 2cm's once mounted. This is at the heel only. Once the toe piece is drilled it is immovable without redrilling. To adjust bindings at both the toe and heel you will need a Rail Flex design.http://www.tyrolia.comhttp://www.fischerskis.com/en/