This paper adopts a systems approach to study how millimeter wave (mmWave) radio transmitters on UAVs provide high throughput links under typical hovering conditions. With Terragraph channel sounder units, we experimentally study the impact of signal fluctuations and sub-optimal beam selection on a testbed involving DJI M600 UAVs. From the hovering-related insights and the measured antenna radiation patterns, we develop and validate the first stochastic UAV-to-Ground mmWave channel model with UAVs as transmitters. Our UAV-centric analytical model complements the classical fading with additional losses expected in the mmWave channel during hovering, considering 3-D antenna configuration and beamforming training parameters. We specifically consider lateral displacement, roll, pitch, and yaw, whose magnitude vary depending on the availability of specialized hardware such as real-time kinematic GPS. We then leverage this model to mitigate the hovering impact on the UAV-to-Ground link by selecting a near-to-optimum pair of beams. Importantly, our work does not change the wireless standard nor require any cross-layer information, making it compatible with current mmWave devices. Results demonstrate that our channel model drops estimation error to 0.2 percent, i.e., 18x lower, and improves the average PHY bit-rate by 10 percent when compared to existing state-of-the-art channel models and beamforming methods for UAVs.