I'll bet $25 it is not the NAV radio.

Do what George says, open the ground cable and insert a meter - I simply can't find it now, but the specification is, I am 99% sure, "not to exceed 40 mA", that is, .04 amp.

Are there ANY aftermarket mods to the sound system? Is there an aftermarket "push button start" or alarm system or remote starter? If not, I'd suspect leaky diode(s) in the alternator.

Why was the battery replaced? That is, what have you been chasing?