If you can't get from Auckland to Wanganui without topping up no matter which route you take then either you've been really hammering it all the way or there's something wrong with the car. I've regularly driven from Hamilton to the Kapiti Coast and back in a SV6 and have never ever needed to fill up along the way. I fact I regularly get back the Levin (where fuel is cheap down that way) to fill up.
I'd avoid SH 1 like the plague. I'd be going to Ngaruawahia, then via Horotiu and Ngaruawahia Roads to SH 39 to Otorohanga, SH 3 to Te Kuiti and Eight Mile Junction, SH 4 Taumarunui to Raetihi to Wanganui. You'll enjoy the drive and there's places to stop to admire the view as well. Good cafes in Otorohanga, Te Kuiti, Taumarunui, and probably Raetihi, (haven't stopped there).