the soft X-ray region relies on frequency multiplication, a scheme known as high-gain-harmonic-generation (HGHG) [@HGHG1; @HGHG2]. In a HGHG FEL, the radiation output is obtained from a coherent subharmonic seed laser pulse. Consequently, the optical properties of HGHG FELs are expected to reflect the characteristics of the high-quality seed laser. Echo-enabled harmonic generation (EEHG) is a recent, promising technique for efficient harmonic generation [@EEHG1; @EEHG2]. The key advantage of EEHG over HGHG is that the amplitude of the achieved microbunching factor decays slowly with an increasing harmonic number. Consequently, as concerns electron beam physics issues, EEHG allows for the generation of fully coherent radiation at soft X-ray wavelengths with a single upshift stage, and using a conventional optical laser system. The remarkable up-frequency conversion efficiency of the method has stimulated wide interest to generate near transform-limited soft X-ray pulses. Several EEHG FEL projects are now under development [@LCLS2E]-[@FLEEHG]. A typical EEHG setup consists of two stages for electron beam phase space manipulation, followed by a radiator. Each stage includes an undulator, which is used to modulate the electron beam in energy with the help of a seed laser, and a chicane following the modulator, which is used to apply energy-dependent 