We report experimental test-beam results on dielectric-loaded waveguide detectors that utilize coherent microwave Cherenkov (Askaryan) signals to time and characterize high energy particle showers. These results are used to validate models and produce high-fidelity simulations of timing plane systems which yield picosecond timing resolution and millimeter spatial coordinates for the shower centroid, while simultaneously being extremely radiation-hard. These timing planes, based on the Askaryan effect in solid dielectrics, are most effective at the high center-of-momentum energies planned for the Future Circular Collider (FCC-hh), and are of particular interest in the forward region due to their high radiation immunity. We use our test beam results and GEANT4 simulations to validate a hybrid microwave detector model, which is used to simulate a reference timing plane design for the FCC forward calorimeters. Our results indicate that 0.5-3 ps particle timing is possible for a wide range of collision products in the reference FCC hadron collider detector, even with current technology.