Axions are highly motivated hypothetical particles beyond the standard model that can be dark matter candidates and address the strong CP problem. Here we search for axion-mediated interactions generated between two separated ^{129}Xe gas ensembles, monitoring and polarizing the ^{129}Xe nuclear spins through spin-exchange interactions with Rb vapor. Our method exploits the magnetic amplification through effective fields from Rb-Xe collisions, increasing the sensitivity for axion-mediated interactions by up to 145-fold relative to conventional methods. Moreover, we employ template filtering to extract exotic interactions with a maximum signal-to-noise ratio. By combining two techniques, axion-mediated interactions are constrained to be less than 10^{-5} of normal magnetic interactions on a length scale of 60 mm. We establish new constraints on the neutron-neutron pseudoscalar couplings for a mass range that expands into the well-motivated "axion window" (10 μeV-1 meV), improving previous constraints by up to 50-fold within it and 118-fold outside it. We further discuss promising applications in searches for other axion-nucleon interactions, including axion dark matter and black hole axion bursts with sensitivity well beyond astrophysical limits by several orders of magnitude.