If your lights are dimming now, how the hell do you think you are going to support 4kw? I have a toyota matrix and now have an 170a alt from ohio gen (with the readouts to prove it) I have a high capacity battery under the hood and I am running (a total of all my amps) 2000wrms and it is just BARELY enough to keep up. You are going to be running double that. I think you might have problems in store. Very similar charging systems we have. I have upgraded my big three with 1/0 also.
I know a bigger alt is probably out of the question (because higher output alts for toyotas are scarce, i had a hard enough time getting mine at a decent price), but you might want to talk to some of the other guys around here on what your other options are.