Based on the connection to one-dimensional interacting particle models--the ASEP and the TAZRP--and the combinatorial objects (multiline queues) that make these connections explicit, a tableau formula was found for the modified Macdonald polynomial in terms of the so-called `queue inversion' statistic. This statistic naturally reflects the dynamics of the TAZRP. In this talk, we present a new tableau formula for the symmetric Macdonald polynomials, using the same queue inversion statistic on non-attacking tableaux. Central to our approach is a probabilistic bijection on non-attacking fillings that enables swapping of entries between columns. Our techniques extend to fillings of composition shapes, leading to symmetry results for permuted basement Macdonald polynomials.