The Stretched-FrOnt-Leg (SFOL) pulse is an advanced distance measuring equipment (DME) pulse that offers superior ranging accuracy compared to conventional Gaussian pulses. Successful SFOL pulse transmission has been recently demonstrated from a commercial Gaussian pulse-based DME in low-power mode utilizing digital predistortion (DPD) techniques for power amplifiers. These adjustments were achieved through software modifications, enabling SFOL integration without replacing existing DME infrastructure. However, the SFOL pulse is designed to optimize ranging capabilities by leveraging the effective radiated power (ERP) and pulse shape parameters permitted within DME specifications. Consequently, it operates with narrow margins against these specifications, potentially leading to non-compliance when transmitted in high-power mode. This paper introduces strategies to enable a Gaussian pulse-based DME to transmit the SFOL pulse while adhering to DME specifications in high-power mode. The proposed strategies involve use of a variant of the SFOL pulse and DPD techniques utilizing truncated singular value decomposition, tailored for high-power DME operations. Test results, conducted on a testbed utilizing a commercial Gaussian pulse-based DME, demonstrate the effectiveness of these strategies, ensuring compliance with DME specifications in high-power mode with minimal performance loss. This study enables cost-effective integration of high-accuracy SFOL pulses into existing high-power DME systems, enhancing aircraft positioning precision while ensuring compliance with industry standards.