This inverter has a square-wave output. Some electronic products won't work properly when powered by it.
Use two heatsinks, one for each side. Then the transistors can be bolted to the heatsinks with thermal grease but no insulators, then insulate the heatsinks from each other and from the grounded metal case. Then the cooling will be best.
Mount the 0.1 ohm emitter resistors on the heatsinks soldered to each emitter and to a terminal strip. Connect the terminal strip to ground (- of the battery) with a very thick wire and connect it to the ground of the circuit board with a thin wire.
Bolt a terminal to each heatsink and connect them to the transformer with thick wire.
Connect together the 50A fuse and switch with thick wire.
Connect the + of the battery to the fuse with thick wire.
Connect the switch to the transformer with thick wire and connect the switch to the circuit board with thin wire.
Connect the output of the opamps to the bases of the pre-driver transistors with thin wires.
Where are you going to get the huge and expensive transformer?