It makes perfectly sense that the wave form does change when you applies inductive load to output. Remember that an inductor tries to prevent fast change in current. Also if your drawing is correct, there is time spaces where at least one end of either halfbridges just floats. That will surely make a lot of ripple because of the type of load.
It should helpto put a cap in parallell to the load, but don't let the overall load being in resonance at the chopping frequenzy.