Correlated magnetic noise from Schumann resonances threatens to contaminate the observation of a stochastic gravitational-wave background in interferometric detectors. In previous work, we reported on the first effort to eliminate global correlated noise from the Schumann resonances using Wiener filtering, demonstrating as much as a factor of two reduction in the coherence between magnetometers on different continents. In this work, we present results from dedicated magnetometer measurements at the Virgo and KAGRA sites, which are the first results for subtraction using data from gravitational-wave detector sites. We compare these measurements to a growing network of permanent magnetometer stations, including at the LIGO sites. We show the effect of mutual magnetometer attraction, arguing that magnetometers should be placed at least one meter from one another. In addition, for the first time, we show how dedicated measurements by magnetometers near to the interferometers can reduce coherence to a level consistent with uncorrelated noise, making a potential detection of a stochastic gravitational-wave background possible.