I'm afraid you've seized on something out of context as support for your assertions, where it really isn't.
In particle physics, lifetime measurements of particles are made at resolution below a picosecond. These lifetime measurements are a quite direct verification of special relativity. The relativistic effect on the particle lifetimes and trajectories are readily observable. This is also observed in cosmic ray muons.
Your assertions that special relativity has not been verified by experiemt and observation are simply incorrect.