This paper presents multichannel quantum defect theory (MQDT) models for highly excited Rydberg states of $^{174}$Yb and $^{171}$Yb with $L \leq 2$, validated by experimental measurements of Stark shifts, magnetic moments, and Rydberg interactions. The models are used to compute interaction potentials between Yb atoms, showing excellent agreement with direct measurements in an optical tweezer array. The study identifies an anomalous Förster resonance in the $^{171}$Yb $F = 3/2$ Rydberg state that degrades gate fidelity, and identifies a more suitable $F = 1/2$ state, achieving a state-of-the-art controlled-Z gate fidelity of $\mathcal{F} = 0.994(1)$. The work establishes a foundation for quantum computing, simulation, and entanglement-enhanced metrology with Yb neutral atom arrays. The MQDT models accurately predict Rydberg state energies, matrix elements, polarizabilities, and interactions, enabling precise predictions for complex atomic systems like $^{87}$Sr and lanthanide atoms. The results demonstrate the importance of high-precision spectroscopy and modeling for quantum technologies.This paper presents multichannel quantum defect theory (MQDT) models for highly excited Rydberg states of $^{174}$Yb and $^{171}$Yb with $L \leq 2$, validated by experimental measurements of Stark shifts, magnetic moments, and Rydberg interactions. The models are used to compute interaction potentials between Yb atoms, showing excellent agreement with direct measurements in an optical tweezer array. The study identifies an anomalous Förster resonance in the $^{171}$Yb $F = 3/2$ Rydberg state that degrades gate fidelity, and identifies a more suitable $F = 1/2$ state, achieving a state-of-the-art controlled-Z gate fidelity of $\mathcal{F} = 0.994(1)$. The work establishes a foundation for quantum computing, simulation, and entanglement-enhanced metrology with Yb neutral atom arrays. The MQDT models accurately predict Rydberg state energies, matrix elements, polarizabilities, and interactions, enabling precise predictions for complex atomic systems like $^{87}$Sr and lanthanide atoms. The results demonstrate the importance of high-precision spectroscopy and modeling for quantum technologies.