Achieving high energy resolution in spin systems is important for fundamental physics research and precision measurements, with alkali-noble-gas comagnetometers being among the best available sensors. We found a new relaxation mechanism in such devices, the gradient of the Fermi-contact-interaction field that dominates the relaxation of hyperpolarized nuclear spins. We report on precise control over spin distribution, demonstrating a tenfold increase of nuclear spin hyperpolarization and transverse coherence time with optimal hybrid optical pumping. Operating in the self-compensation regime, our ^{21}Ne-Rb-K comagnetometer achieves an ultrahigh inertial rotation sensitivity of 3×10^{-8} rad/s/Hz^{1/2} in the frequency range from 0.2 to 1.0 Hz, which is equivalent to the energy resolution of 3.1×10^{-23} eV/Hz^{1/2}. We propose to use this comagnetometer to search for exotic spin-dependent interactions involving proton and neutron spins. The projected sensitivity surpasses the previous experimental and astrophysical limits by more than 4 orders of magnitude.