There may be a relatively simple solution.
A frame which rigidly attached to the brace, and through the use of a C
( or open front D) shaped " dropout" at the other end, with the opening large
enough to accommodate a handlebar. A large carabiner with the spring
removed may be a good template.
The opening would allow the handlebar to be be grasped/hooked in either the
push or pull mode, yet allow the brace to be be quickly disengaged, with a
relatively natural movement.
This device would be able to both support the riders weight to a degree when pushed
against the handlebar.
It would also allow the rider to pull back with their shoulder against the handlebar
when needed, likely on ascents.
The length of of the arms could be fit to the system is such a way as to incorporate
the velcro/glove solution as well. This dropout would be made to fit both on the top
flat of a bar, but also to fit on the drop or tourist type bar. It may need to have some
pivot built in to do this.
Just some ideas.