We report experimental test-beam results on dielectric-loaded waveguide detectors that utilize microwave Cherenkov 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 time tags and millimeter spatial coordinates for the shower centroid. 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 beam test 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.