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Optically addressable paramagnetic defects in wide-band-gap semiconductors are promising platforms for quantum communications and sensing. The presence of avoided crossings between the electronic levels of these defects can substantially alter their quantum dynamics and be both detrimental and beneficial for quantum information applications. Here we present a joint theoretical and experimental study of the quantum dynamics of paramagnetic defects interacting with a nuclear spin bath at avoided crossings. We find that we can condition the clock transition of the divacancies in SiC on multiple adjacent nuclear spins states. We suppress the effects of fluctuating charge impurities and demonstrate an increased coherence time at clock transition, which is limited purely by magnetic noise. Our results pave the way to designing single defect quantum devices operating at avoided crossings.