Our molecular dynamics analysis of Xe_{147-5083} clusters identifies two mechanisms that contribute to the yet unexplained observation of extremely highly charged ions in intense laser cluster experiments. First, electron impact ionization is enhanced by the local cluster electric field, increasing the highest charge states by up to 40%; a corresponding theoretical method is developed. Second, electron-ion recombination after the laser pulse is frustrated by acceleration electric fields typically used in ion detectors. This increases the highest charge states by up to 90%, as compared to the usual assumption of total recombination of all cluster-bound electrons. Both effects together augment the highest charge states by up to 120%, in reasonable agreement with experiments.