If the area below the counter are concealed, it seems to me that you could put in a branch tailpiece. That would connect to tubing that goes into the wall and up. It would not connect to the vent system. The point would be to allow the air to exit from the tailpiece area.
There may be rules against that for all I know. It would function well.
Another idea that would work would be a conventional stopper.
That would open enough space to let air out as water enters. OK, I know that would not go over unless the homeowner read it was in fashion.
Is there a popup drain for no-overflow vessel sinks where the user can easily lift out the pop-up to allow faster draining when that is needed? If not, there should be.