Family of 6 on Euro600 week net
My first thought on reading your post was about that Charles Dickens character who repeatedly said "Income 2/6d, outgoings 3/-, unhappiness; income 2/6d, outgoings 2/6d, happiness!"
From my professional field I happen to know that a recent spate of sociological research in the US and UK has shown conclusively that 'having more' has NOT resulted in contentment, but in its opposite, and researchers are speculating that this is due to people having nothing to aim for or aspire to.
That said, as someone who for years was self-employed with low income, or on short-term (teaching) contracts, I empathise with your wish to be less vulnerable when big bills (a roof to be mended, or a medical emergency) come, so am offering this.
One unexpectedly-large drain on financial resources is highly-processed, highly-packaged foods. You may be someone who grows your own organic veg in your back garden, or 'cooks from scratch'?.....in which case this advice is redundant. Did you know for example potato crisps cost more per kilo than finest caviar? Unpackaged fruit and veg cost less per kilo; buying pizza bases, tomato puree and toppings of your choice (cheese to grate, sliced ham or pepperoni, green peppers, etc.) gives you a better product for about quarter the price without additives and salt (which all health advice these days is telling us we get too much of!). Today I queued in a Boots Chemist (I live in the UK) behind a young woman who was buying a small plastic bag of apple slices, and she was handing over £1.50 (that's sterling!) for less than the weight of one fresh apple (plus, of course, the food value of fruit and vegetable plummets as soon as you slice it, so she was paying a high price for a plastic bag she was going to drop on the street outside). Filled rolls, for example, cost about £2.50 each (or £10 for 4 youngsters) for a length of french bread with - say - tuna and mayonnaise. The ingredients are not the best. or on the other hand you can instead make fresh tasty sandwich lunches for all 4 youngsters for the price of ONE french stick, ONE small tin of good quality (dolphin friendly) tuna, and quality mayonnaise (even cheaper if you make this yourself, which is a simple process). All the pre-prepared sachets and jars of sauces costing nearly £2 each can be prepared at home for a fraction of the cost.
Initial outlay - for seeds and young plants for a garden to grow fruit and basic vegetables, and on ingredients for real cooking - seems steep, and most people won't go to the bother, but this is the biggest source of
That's my main offering. You've said you work nights and your wife works days so perhaps pre-prepared heavily-packaged foods are your staple (and youngsters don't seem to have any concept of cooking for themselves). It makes a HUGE difference!
The other thing that comes to mind (though I'm sure you've already seen to this - you sound very thorough and organised) is energy-conservation! The huge difference having cavity-walls lagged, insulating roof cavity to the maximum, opening the fridge just ONCE to take out everything needed (as opposed to repeatedly opening the door taking out single items) hanging thick curtains, putting draught-excluders on outer doors, NOT switching lights on and off repeatedly during the evening (the highest consumption of energy is in the switching on/off, I was told recently!) - all adds up.
Hope this is helpful!