I'm also in NZ and everything you say is true, except wtf $1k in electric and gas?! I'm not a conservative energy user, and I'm paying around $280 (mid winter) for a family of 4. Hard to believe/understand the $1k remark.
I'm working on getting her to understand that we don't need to heat rooms we don't use.
But $280 is cheaper than I pay during summer. I'm averaging about 20KWHs in the summer. At the moment it's closer to 75KWHs per day. Our hot water is all gas. About 1 x $150 bottle per month in the summer. That moves up to 1 per week in the winter.
Double glassing is in the wish list. Then wall insulation. But we have a mortgage and an asbestos roof to deal with first.
That's a lot of energy per day, mate. I'm in the US and not particularly careful with usage and I'm averaging about 25KWH a day. You might want to get a usage meter that lets you check various appliances/lights/switches in real time to find the heavy usage
We do need to get down to less freezers but we have some home kill that we need to get through first.
I normally don't stay in places with a dryer and just let things air dry. If you're running heating/ac, they normally lower humidity so things dry really fast anyway.
6 a day is on the high side. It's probably an overestimate.
When there are no new borns we might dry 3 loads a week.
But the house is a work in progress. The curtains blow on a windy day.