This paper introduces a large air-gap capacitive wireless power transfer (WPT) system for electric vehicle charging that achieves a power transfer density exceeding the state-of-the-art by more than a factor of four. This high power transfer density is achieved by operating at a high switching frequency (6.78 MHz), combined with an innovative approach to designing matching networks that enable effective power transfer at this high frequency. In this approach, the matching networks are designed such that the parasitic capacitances present in a vehicle charging environment are absorbed and utilized as part of the wireless power transfer mechanism. A new modeling approach is developed to simplify the complex network of parasitic capacitances into equivalent capacitances that are directly utilized as the matching network capacitors. A systematic procedure to accurately measure these equivalent capacitances is also presented. A prototype capacitive WPT system with 150 cm2 coupling plates, operating at 6.78 MHz and incorporating matching networks designed using the proposed approach, is built and tested. The prototype system transfers 589 W of power across a 12-cm air gap, achieving a power transfer density of 19.6 kW/m2.