Punching shear is inversely proportional to periphery of the critical section and effective depth of the section. As we increase the size of the perimeter the shear force acting at critical section also decreases.Therefore only option left in your case is to increase the diameter of capital or increase the drop panel size.
Shear reinforcement is the answer, but it has to be a special kind. Because flat slabs are so thin, not only are conventional stirrups difficult to place, they are very poor because of the slip involved - slip at the corner bends. The answer is 'headed studs', in the form of pre-fabricated stud rails. The studs have large heads (more than conventional shear studs used for steel beam - slab composite action), to reduce bearing stress. These studs are very efficient shear reinforcement, with low slip. If you web-search for 'stud rail reinforcement' or the like, you will find a lot of manufacturers and plenty of pictures. They are widely used in seismic areas of North America (for both prestressed and reinforced slabs), because even flat slabs laterally braced by seismic frames, walls or bracing can suffer cyclic earthquake induced cracking and punching failure around the columns. Amin Ghali of the University of Calgary published quite a few papers on the subject in the 1990s.