We report a gain-switched diode-seeded thulium doped fiber master oscillator power amplifier (MOPA) producing up to 295-kW picosecond pulses (35 ps) at a repetition rate of 1 MHz with a good beam quality (M ~1.3). A narrow-band, grating-based filter was incorporated within the amplifier chain to restrict the accumulation of nonlinear spectral broadening and counter-pumping of a short length of large-mode-area (LMA) fiber was used in the final stage amplifier to further reduce nonlinear effects. Finally, we generated watt-level >2.5-octave supercontinuum spanning from 750 nm to 5000 nm by using the MOPA output to pump an indium fluoride fiber.