At each fixed Hamiltonian, P, Q, and Weyl coherent-state path-integral constructions represent one exact propagator under the relevant ordering and limiting conditions, while generating different Hamiltonian symbols, stationary structures, correction phases, and fluctuation prefactors at the semiclassical level. This paper asks what explanatory significance should be assigned to those representation-dependent structures when the exact quantum target is shared. It treats known exact-equivalent alternatives as relational controls on explanatory attribution: comparison can separate dependence on the physical system from dependence on representational organisation. Existing accounts of model explanation, equivalent reformulations, perspicuity, and path interpretation provide resources for this assessment, but do not by themselves settle the cross-representation case. I develop a case-specific, contrast-sensitive method that compares the common target, approximation regime, explanandum, physical intervention, and dependencies displayed by each candidate model. The method is applied to a nonlinear double-wall barrier in which the dimensionless barrier strength is increased from V_0 = 1.0 to V_0 = 1.2, with the geometry, endpoints, time, coherent-state width, and representational conventions held fixed. The three representations exhibit the same algebraic 20 percent scaling of the local force because the barrier parameter enters linearly, but they yield different absolute local fields and different reduced-symbol contributions to a leading short-time phase/exponent contrast. These results establish structural sensitivity to representation within a shared physical intervention, not three experimentally distinct predictions, completed transition amplitudes, or globally solved complex trajectories. When the exact-level explanandum, contrast, and physical dependence are shared, the strongest interpretation is one explanation organised through different representational structures. Distinct model explanations remain possible only for physically meaningful approximation-level explananda supported by independently justified contrasts or non-redundant dependencies. The paper therefore offers a comparative test, not a general account of path ontology or explanatory pluralism. The conclusion is limited to this coherent-state case and to local, short-time diagnostics.