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Newly-born pulsars offer favorable sites for the injection of heavy nuclei, and for their further acceleration to ultrahigh energies. Once accelerated in the pulsar wind, nuclei have to escape from the surrounding supernova envelope. We examine this escape analytically and numerically, and discuss the pulsar source scenario in light of the latest ultrahigh energy cosmic ray (UHECR) data. Our calculations show that, at early times, when protons can be accelerated to energies E>10^20 eV, the young supernova shell tends to prevent their escape. In contrast, because of their higher charge, iron-peaked nuclei are still accelerated to the highest observed energies at later times, when the envelope has become thin enough to allow their escape. Ultrahigh energy iron nuclei escape newly-born pulsars with millisecond periods and dipole magnetic fields of ~10^(12-13) G, embedded in core-collapse supernovae. Due to the production of secondary nucleons, the envelope crossing leads to a transition of composition from light to heavy elements at a few EeV, as observed by the Auger Observatory. The escape also results in a softer spectral slope than that initially injected via unipolar induction, which allows for a good fit to the observed UHECR spectrum. We conclude that the acceleration of iron-peaked elements in a reasonably small fraction (< 0.01%) of extragalactic rotation-powered young pulsars would reproduce satisfactorily the current UHECR data. Possible signatures of this scenario are also discussed.