First of let me start with I don't to be taken as rude, dismissive or bossy and I no trying to poo on your idea.
Ok where to start, I see 3 problems with the current design. The first and most obvious is that is is overly complex and there for very fragile. Each place where you have the plasma conduits changing direction is a point of rupture. This design is much more vulnerable to coolant leaking or full on core breaches.
Second is that you can't bring the matter and anti mater streams together outside of a dilithium crystal. The interaction of the plasma streams within the crystal is what attenuates the reaction temporarily preventing the total annihilation of the plasma till it reaches the nacelles. In the current design you will need 3 more reaction chambers with their own dilithium crystals.
Thirdly is that this is all unnecessary as they all ready figured out how to do what you want in the TV show. In the TNG episode Galaxies Child The boost the power by bouncing multiple plasma streams around in side the constrictor elements. This was to be a feature of the next generation of warp cores. Those next generation cores can be seen fitted to Defiant and Enterprise E. Defiant has 4 lobed constrictor elements and Enterprise as 6 lobed elements. Each one of these lobes is and additional channel that you can run another plasma stream down or up in the case of the anti matter. This allows Defiant to generate 5 times the warp plasma and enterprise to generate 7 time the warp plasma. Hope this helps after all is a great idea.
