Electrical – Voltage spikes in h-bridge inverter square wave output

Yes, at this input voltage a center tapped primary with low side switches on the ends seems like the way to go. For feedback, I'd look at opto-isolators first. Put something on the output side that can detect whether the voltage is above or below the regulation threshold and drive the opto accordingly. On the primary side, a simple control method is to simply stop the oscillations when the opto signal indicates the output is high. If you can live with some ripple, this should be effective, simple, and efficient.

You can use a 2nd order low pass filter made from an inductor (in series with the AC) and a capacitor to neutral. You will also need a resistor: -

^{simulate this circuit – Schematic created using CircuitLab}

1 Henry and 10uF form a 2nd order low pass filter that will attenuate the higher order frequencies from the sq wave and make the output signal more sinusoidal in nature. It might work fine or it still might give your TV problems if it is particularly sensitive to harmonics.

The resistor is needed to keep the Q of the circuit low and prevent high ringing voltages.

Q = \$\dfrac{1}{R}\sqrt{\dfrac{L}{C}}\$ = 3.16 using the values above.

Q needs to be about unity so I'd advise to make C bigger and L proportionally smaller but be aware that the value of resistance is in series with the TV and whatever current the TV takes, it flows through the resistor. For instance, 110 watts needs 0.5 amps from 220 V and this means the I^2R losses in the resistor are 25 watts - choose big wirewound resistors.