Hi Alun,
For about 50ns of each output transition, both Mosfets will conduct 10A to hundreds of amps from the power supply to ground. That's why I suggested using a SMPS IC with its dead-time controlled to avoid both Mosfets in series conducting at the same time.
The little 555 is bad by itself since it conducts about 400mA from the supply to ground through its output transistors in series across the supply.

;D
PS. Won't the bridge-connected load receive almost 14VAC peak-to-peak? ???
I guess a 14V peak-to-peak square wave has the same heating effect for a resistive load as a 5V RMS sine wave or 5VDC. To get 7V effective output it should be boosted by 1.4 times.