Push-and-slide tasks carried out by fully-actuated aerial robots can be used for inspection and simple maintenance tasks at height, such as non-destructive testing and painting. Often, an end-effector based on multiple non-actuated contact wheels is used to contact the surface. This approach entails challenges in ensuring consistent wheel contact with a surface whose exact orientation and location might be uncertain due to sensor aliasing and drift. Using a standard full-pose controller dependent on the inaccurate surface position and orientation may cause wheels to lose contact during sliding, and subsequently lead to robot tip-over. To address the tip-over issue, we present two approaches: (1) tip-over avoidance guidelines for hardware design, and (2) control for tip-over recovery and avoidance. Physical experiments with a fully-actuated aerial vehicle were executed for a push-and-slide task on a flat surface. The resulting data is used in deriving tip-over avoidance guidelines and designing a simulator that closely captures real-world conditions. We then use the simulator to test the effectiveness and robustness of the proposed approaches in risky scenarios against uncertainties.