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Well...I noticed your looking at Mk3 injectors. I'm not sure about them but I know in the IS (which should be the same rail as the Gs3) that the Rc injectors I used to use needed to be machined on the lathe to work. A general rule of thumb on injectors for the 2jz is 1cc/1hp, so running 550cc will be plenty for making 350hp. Idk what your doing about fuel management but the further out you get (larger) on injectors the more correction you are going to need to make, again, depending on what fuel management you have there is a limit on how far it can adjust.
MKIII injectors require a resistor box, they're low impedance.
440cc will do the job since your not boosting over 350hp.
RC Engineering 440cc high impedance saturated fuel injectors.
Model number SL4-440 are direct drop in.