This paper introduces an interference-free multi-stream transmission architecture leveraging stacked intelligent metasurfaces (SIMs), from a new perspective of interference exploitation. Unlike traditional interference exploitation precoding (IEP) which relies on computational hardware circuitry, we perform the precoding operations within the analog wave domain provided by SIMs. However, the benefits of SIM-enabled IEP are limited by the nonlinear distortion (NLD) caused by power amplifiers. A hardware-efficient interference-free transmitter architecture is developed to exploit SIM's high and flexible degree of freedom (DoF), where the NLD on modulated symbols can be directly compensated in the wave domain. Moreover, we design a frame-level SIM configuration scheme and formulate a maxmin problem on the safety margin function. With respect to the optimization of SIM phase shifts, we propose a recursive oblique manifold (ROM) algorithm to tackle the complex coupling among phase shifts across multiple layers. A flexible DoF-driven antenna selection (AS) scheme is explored in the SIM-enabled IEP system. Using an ROM-based alternating optimization (ROM-AO) framework, our approach jointly optimizes transmit AS, SIM phase shift design, and power allocation (PA), and develops a greedy safety margin-based AS algorithm. Simulations show that the proposed SIM-enabled frame-level IEP scheme significantly outperforms benchmarks. Specifically, the strategy with AS and PA can achieve a 20 dB performance gain compared to the case without any strategy under the 12 dB signal-to-noise ratio, which confirms the superiority of the NLD-aware IEP scheme and the effectiveness of the proposed algorithm.