basically, you don't need to regulate the power going into the battery because it's deep cycle, and it will discharge at the rate it's charging at due to the dc/ac converters. the diode will ensure no feedback electricity if the power goes out, think about it, the battery is in a closed loop, if it doesn't have charge going through the loop, it'll give off energy and cause a short circuit if you don't have a diode to make sure the current only goes one way.
Also, the 120V AC will be in phase because the circuit is parallel, and also the converter is between the first branch and the battery, so one side of the parallel circuit is dc, and the other is ac, and then converted again before the circuit is put back together. The harmonics will be fine because the current will not be broken at all, especially if the battery is fully charged the sine wave will not be affected. Keep it simple, putting too much BS in it will only make it harder.
-Zoson
EDIT: oh yeah, and would you guys freakin' spell my name right? (it's a pet peeve of mine.)