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The detected Gaia systems hosting compact objects challenge standard models of binary star evolution. In particular, if the observed black hole (BH) systems evolved in isolation, they are expected to have undergone a mass transfer phase. Given their highly unequal masses, such mass transfer is dynamically unstable within standard models, leading to a stellar merger or a short-period binary. In contrast, the observed systems have much wider orbits than predicted, making their formation within conventional evolutionary frameworks difficult to reconcile. Using detailed binary evolution calculations, we test whether nonconservative mass transfer, in which most of the mass is lost from the system carrying the specific angular momentum of the donor's center of mass, can explain the properties of two Gaia BH systems. This mass-loss geometry differs from standard isotropic re-emission from the accretor's vicinity. We find that our mass-loss geometry model reproduces the orbital periods of the two Gaia BH systems remarkably well over a wide range of initial conditions, offering a plausible formation pathway. We speculate this may point to enhanced eruptive mass loss, potentially driven by high-opacity subsurface layers in the donor prior to Roche-lobe overflow, consistent with preferentially bipolar outflows observed in luminous blue variables. Alternatively, it may indicate the need for more sophisticated mass-transfer prescriptions that account for highly unequal Roche-lobe sizes, subsynchronous rotation, and possible self-accretion. Similar mechanisms may operate in other post-mass-transfer systems facing analogous evolutionary challenges, including Gaia neutron-star and white-dwarf binaries, stripped-envelope Wolf─Rayet stars, and low-mass X-ray binaries.