Far-detuned frequency allocations in fixed-frequency superconducting processors mitigate spectral crowding but constrain cross-resonance interactions at practical drive amplitudes. Here, we demonstrate that a single strong drive induces a large XX-YY interaction in the far-detuned regime, while a weak second tone tunes the accompanying ZZ phase. The interaction realizes a 150-ns √bSWAP gate, which can directly prepare a maximally entangled state from the ground state. For the implementations on the same qubit pair at matched drive strengths, cross resonance gives a shorter CNOT operation, while √bSWAP gives a 33% shorter SWAP operation with a higher IRB fidelity. The multilevel theory further predicts a regime where stronger driving can yield a speed advantage for CNOT as well, a possibility absent in the two-level model. As an application of the XX-YY interaction, we also demonstrate two-spin squeezing beyond the standard quantum limit through two-axis countertwisting. The interaction realized here complements cross resonance and offers a route to efficient gate synthesis and quantum simulation of interacting spin systems.