Ive only read up to pay 6 but thoughts are:
Can you write down a diary listing what you buy and the cost and then after a week look back at it and reflect ont it to see what can be changed.
$700 is the same as $100 per day maybe instead of doing a weekly shop do a twice a week shop and look for special offers. I think I remember when I was in Coles earlier this year they did a feed your family for x amount and showed cheap recipe ideas. Not sure if they still do that. IGA I also remember being more expensive then Coles unless they had special offers on.
Go to butchers for meat. I remember when I was in Sydney earlier this year it was a lot cheaper to buy from the butcher for meat and the selection was also better.
Drop a band level, instead of maybe premium or semi premium brands drop a brand as this could save money.
Maybe list a breakdown of a weeks shop on here and others can suggest the cheaper place to buy the products from?
I am sure with determination the $700 can be reduced a lot.
Good luck :)