After seeing your schematic, I can't imagine a better way to achieve your objective. It could possibly be realized by using switch mode techniques but, in view of the high voltages and currents that would involve a massive design and development exercise, and the components would be expensive.
As the problem stated on the schematic is that the transformers are overheating, you could look at ways of improving the rectification efficiency, but that would require six large inductors, one between each bridge rectifier and capacitor bank or one very large inductor in series with the capacitor bank
The other approach would be to implement an efficient cooling system for the transformers. If forced air cooling was not sufficient, oil cooling may be possible but it would be important to use transformer oil compatible with your transformers. Can you post a picture of the physical set up and show one of the transformers in detail.
While your schematic is pretty clever and well drawn, it may be better to connect all six transformer secondaries in parallel and use just one high current high voltage bridge rectifier. This should ensure that the transformers current shared better.
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