How is the inverter wired to 12v? I also use powered speakers from a MSW 150w inverter, but it is just plugged into the 12v socket in the Winegard. Thing is the 12v plug has a fuse in it, so I think that protects the inverter from anything funny happening to its 12v input and so anything plugged into the 120v output (maybe). Of course the Winegard socket is also on a fuse in the DC fuse panel marked TV.
Could you test the output of the inverter with a meter just as the converter goes to 14.8 and see if it spikes?