The rotation will stay the same left hand and I will keep my belt drive thanks.
You apparently already have this engine, and a CH2 belt.
If you additionally already have the LH Falcon blades that you referenced, this statement kind of goes without saying.
If you do not, it
may be worth reconsidering your desire to stay left handed given an unknown to you, tidbit of information.
That would be dependent on your commitment/need to pulling every last bit of available power out of your new engine.
You won't find a 2.3 gear to fit your CH2 box. There were 1.5 and 1.77 pulleys sets for the CH2, but 2.0 was as good as it got.
The CH2 runs a 4" wide belt, whereas the CH3 runs a 5" belt. Consequently the CH2 housing will not accommodate the CH3's bigger pulleys and are therefore not a option. I think the available choices with the CH3 were/are 2.0 , 2.3, and 2.5.
If you already have your prop, all is not lost. Those Falcon blades push more effectively with more pitch compared to set flatter. With a design of 2450 pRPM and then pitched to 4900, that puts you past your peak torque but will likely leave a little HP on the table. No harm done, perhaps longevity is increased. My bet is that in the end, you will find your best push is short of your max eRPM.
If you don't already have that prop
and you want to squeeze every newton of push out of your new engine, you will need another ratio. No difference in prop price LH or RH, so that's a push. Don't know how pricing currently varies between gear and belt. The fact either way, is that gear offers more ratios and is lighter.
In spite of 2.3 being a better match; if it were me and I already had that prop, I'd run it, but then I'm admittedly a bit of a CSOB.