We searched through a seven-million cubic-parsec volume surrounding each of the four nearest young open clusters with ages from 40 to 80 Myr to identify both the current and past members of the clusters within the Gaia EDR3 dataset. We find over 1,700 current cluster members and over 1,200 candidate escapees. Many of these candidates lie well in front and behind the cluster from our point of view, so formerly they were considered cluster members, but their parallaxes put them more than 10 pc from the centre of the cluster today. We found two candidate high-mass white dwarfs that may have escaped from the alpha Persei cluster and several candidate main-sequence-white-dwarf binaries associated with the younger clusters, NGC 2451A, IC 2391 and IC 2602. All of these objects require spectroscopic confirmation. Using these samples of escapee candidates, we develop and implement a novel technique to determine the ages of these clusters and the Pleiades using kinematics with typical uncertainties of $5-7$ Myr. For all five clusters, this kinematic age is younger than the age estimated with isochrones but within the uncertainties of the isochrone fitting. We find for the clusters that travel far from the Galactic plane (the Pleiades, NGC 2451A and IC 2602), the formation of the cluster coincides with when the cluster was in the Galactic plane within a few Myr, supporting these age determinations.