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Abrikosov vortices in Fe-based superconductors are a promising platform for hosting Majorana zero-energy modes. Their adiabatic exchange is a key ingredient for Majorana-based quantum computing. However, the adiabatic braiding process cannot be realized in state-of-the-art experiments. We propose to replace the infinitely slow, long-path braiding by a procedure that only slightly moves vortices in a special geometry without actually physically exchanging the Majoranas, like a Majorana carousel. Although the resulting finite-time gate is not topologically protected, it is robust against variations in material-specific parameters and in the braiding speed. We prove this analytically. Our results carry over to Y junctions of Majorana wires.