You should be able to run all of those. My home is "off the grid" and I used a modified sine wave inverter for many years to power everything except washer, dryer and well (ran a generator for them).
Sometimes (depending on inverter model) you can get buzzing or lines on a tv. I also had a "situation" with a compact fluorescent light and a cheap surround sound amplifier: they were only a few feet apart and when the light was turned on, it would make the amp do weird things. Finally got a better amp and the problem went away.
Currently I use that old inverter to power a jet pump for our water pressure, and two sine-wave inverters (one for lights and entertainment, the other for everything else including washer and dryer).
Oh (on edit) VIN: NICE HOUSEBOAT!!!