The purpose of the two caps is to provide a RF centre tap for the DC supply. Suppose they were replaced with an actual centre tap, then when the upper transistor comes on, the current will flow through the load,from +300V to centre tap. When the lower transistor comes on the current flow through the load is the other way around, from the centre tap to earth. The centre tap has been replaced by the two capacitors which are in series with the load so must be of low impedance and high current rating.
One clue might be how much the supply current changes when the iron bar is stuck in the coil. Without the iron, the current should be low, introducing the iron should then increase the current
You could put a known quantity of water in a cup and time it until it has boiled away. Then you can work out the power to do this and find out how much power you have got.
Frank
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More thoughts:- Change the oscillator frequency to bring the output circuit on tune. I do not think that 500W will heat much iron to red heat, try a loop of thin garden fence wire as a starter.
Frank