Yes, I think you could get 1KW out of this circuit with the following conditions met:
1) The switching FET needs to be a pretty big device (like an IRFP460) with very good heatsinking
2) The switching transformer needs to be pretty serious (like an ETD49), well designed, and close to the PCB
3) You need to add an R-C filter that includes a steering diode (see other flyback SMPS's for an idea how to implement)
4) The 300V supply needs to be quite robust (are you going to use PFC?)
5) Make sure the switching frequency is not too high to have copper losses impact the power level (like maybe 25 to 50KHz)
The small transformer you have a question-mark over looks to be a feedback and Vsupply source. During normal operation, the power FET's switching is coupled through the 22nF/250VAC cap and the transformer generates two voltages - one to supply Vcc, pin 7, of the 3842 IC and the other voltage as feedback to pin 2. It looks like the current sense is set to about 4.5A (1V/0.22ohm Source resistor), so with 300V in, you're at about 1.3KW - on target with your goal.
This looks like a great project to experiment with! Please post your project and findings, if you'd be so kind, and let us know if it works and if so, how it works. I think your "hybrid" idea of using an existing SMPS with some beefy parts added to improve performance and output power is a fantastic idea others might like to follow!
And, if you have the technical know-how, you may also want to write-up a little post about how to do this so others can follow. I believe the main hurdles are the power capabilities of the switching FET, filtering the Drain switching waveforms, properly designing the transformer, adjusting the feedback circuit to cope with the altered supply voltage, providing an adequately powerful high DC voltage (300 in your example), and adjusting the current limiting values (1V sense with a 0.22ohm resistor in your example). If you could elaborate on each of these issues so others could do the same type of modified high-power design, you would be quite the SMPS hero on this forum! Well, okay, "hero" may be a tad much, but you could certainly earn some respect and appreciation. You'd have mine, that's for sure!
I hope my comments and suggestions help you a bit too to make some progress on your project!