Thin-film organic distributed feedback (DFB) lasers processed with elastomeric polymers allow fabrication of flexible and continuously tunable coherent light sources. So far, the realized laser devices fall short on broad continuous tuning range. We demonstrate that the addition of plasticizers to the polymer matrix and the minimization of the thickness of the laser can reduce mechanical impact and, thus, extend the wavelength tuning range to the full gain range of the active medium. A contact-transfer method is used to transfer gently the ultra-thin membrane DFB laser to a silicone support. A continuous tuning of the laser wavelength up to 77 nm in the orange-red spectral range of a single laser dye was achieved by mechanical stretching of the supporting film with a DFB membrane laser on top.