We experimentally demonstrated a type of tunable and switchable harmonic h-shaped pulse generation in a thulium-doped fiber (TDF) laser passively mode locked by using an ultralong nonlinear optical loop mirror. The total cavity length was ～3.03 km, the longest ever built for a TDF laser to our best knowledge, which resulted in an ultralarge anomalous dispersion over 200 ps2 around the emission wavelength. The produced h-shaped pulse can operate either in a fundamental or in a high-order harmonic mode-locking (HML) state depending on pump power and intra-cavity polarization state (PS). The pulse duration, no matter of the operation state, was tunable with pump power. However, pulse breaking and self-organizing occurred, resulting in high-order HML, when the pump power increased above a threshold. At a fixed pump power, the order of HML was switchable from one to another by manipulating the PS. Switching from the 8th up to the 48th order of HML was achieved with a fixed pump power of ～4.15 W. Our results revealed the detailed evolution and switching characteristics of the HML and individual pulse envelope with respect to both the pump power and PS. We have also discussed in detail the mechanisms of both the h-shaped pulse generation and the switching of its HML. This contribution would be helpful for further in-depth study on the underlying dynamics of long-duration particular-envelope pulses with ultralarge anomalous dispersion and ultralong roundtrip time.