I reduced my saturated fats back in November, less meat products, and increased the whole meal / whole wheat which now means we change what we buy, and buy both types of most things. For example 2 types of spaghetti, 2 types of pasta, bread, semi and skimmed milk or vegan milks if I am feeling fancy. I rarely eat beef, or pork now at all, for these things I have swapped to vegan. I am not doing low carb as that's not an issue for me, but this is an example of how it works for our family.
We generally eat the same meals but I will have a different ingredient in mine. So we do burgers, they have beef and I have vegan or vegan, they have cheese, and I low fat and thinner slices, and I will have extra salad no bacon on mine etc. Look at what you all generally eat now and improve what is on your plate. Spag bol, again mine is vegan mince. Pizza there isn't really an alternative, but having less slices is better and again get in your salad and veg etc in its place.
It seems like more cost at first, but it isn't as it all gets eaten in the end, 2 packets of pasta last the same amount of time, it is more dishes though so that's not fun but it can be done.