To address the frequency-dependent rank growth and the resulting loss of compression efficiency when adaptive cross approximation (ACA) is directly applied to the loop-impedance matrix in broadband magneto-quasi-static resistance and inductance (RL) extraction, a basis-transformation-based ACA scheme is proposed. The directional degrees of freedom of vector current basis functions are isolated into three sparse mapping matrices, leaving a dense core matrix that contains only scalar couplings between panels. ACA is then applied exclusively to this core matrix. The formulation is combined with mixed surface meshes, loop-current analysis, and a broadband equivalent surface-impedance model. Numerical results show that the rank and compression ratio of far-field blocks remain nearly frequency independent. For the two-conductor example, the maximum speedups of matrix filling and compression are approximately 6 and 80, respectively. For the FCBGA and FCCSP examples, matrix-generation time is reduced from 89 s to 13 s and from 304 s to 25 s, while peak memory is reduced by 20.8% and 31.3%. The maximum reported deviations of the extracted R and L parameters are 4.6% and 1.73%, respectively.