First thing you should do is: put a fill or solid region to overwrite the poligonconnect design rule. Then, if you can, make a poligon on the other side of the PCB, and connect it to the vias. Also, make sure, the vias are not connected with relief. Remove solder mask on if possible, but of course keep some around the footprint. Extend the copper on top as mucha s possible. You might want to increase the density of the vias. Also, I'm not sure about the diameter you are using, but AFAIK 0.3mm-0.4mm is the best. Somewhere I read that more than two rows of via has very small effect.
If nothing helps, there are SMD heatsinks, which you can solder "around" the component. If you bring the ground plane close (~0.2mm)to the VCC that also helps. How much are you dissipating? How big is the pour you have?