I am now trying this approach and so far it seems to be working. It's been a couple of months and I'm happy to continue taking an extra 30 minutes after my shopping day to save hours through the week.
When I get the vegetables out of the shopping bag, I am immediately washing them and cutting them into cooking size and then popping into a big 7litre container. 3 of these fit perfectly along the bottom shelf of our fridge. I separate different things into these containers from vegetables, fruit, yoghurt's, and leftovers. I do leave certain vegetables whole as we all love carrots, just eating them raw and whole. We go through a bag each week just snacking on carrots, so I cut some and leave a lot whole. I also like to keep Kale in a bunch as I make Kale chips.
Doing this not only gives me more time during the week with my family and less stress at dinner time but it also means I use all of our vegetables up and I don't have waste anymore. These containers keep them fresh. You can also pop a piece of paper towel along the bottom to soak up excess moisture which will prolong the life of the vegetables too.
As I have small children at home with me, when I am about to do all this washing and chopping of vegetables I set up a game for the kids, something that hasn't been out already. Try keep a few things packed away so when you need to distract the kids for a bit, you have something "new" as a novelty. Or if it's been a busy day and they have been out, I will pop on a movie or play school. Anything to give me half an hour where I can get this done as it then saves me hours during the week, which means more time with the kids.