this is such a difficult question isn't it. We would naturally do anything to protect our cats but moving home is such an upheaval especially if there might be no improvement.
My own experience is so similar to all of yours that I felt compelled to post.
I moved home 8 years ago to a a quiet cul-de-sac private lane with only 8 dwellings. The lane which is only wide enough for one vehicle goes past the front doors of three of the cottages including mine.
I thought this would be about as safe as you could possibly get but I was so wrong. Most of my neighbours have daily deliveries from Postmen , DIY stores, Tescoes, Couriers, Milkmen, Grocers, Fresh fish deliveries, meals-on-wheels etc etc . Its like picadilly circus all day long and there are only 8 dwellings !....
Worse still inspite of it being a tiny little private lane everybody charges up and down the lane at over 15-20 mph ? crazy .!..
Its mostly my neighbours that speed as well.
I don't mean to be sexist but out of the 8 dwellings there are 15 drivers 7 female and 8 male. (incl me) out of these 5 men drive at practically a snails pace carefully and consideratly The remaining 10 residents drive very quickly without any thought to children and animals and the 3 disabled residents. Of these 10 there are 3 that drive ridiculously fast and they are all female . Furthermore every one of these 3 females have a pet dog of their own and would obviously dread anything happening to their dog but obviously are complety unaware of the risk to the cats down the lane even though I have asked them to slow down many times.
Now make of this what you will but I live on the edge of my seat the whole day and night waiting for a screech of tyres outside my kitchen door. ( straight on to the lane) Both my cats are out the lane all the time dispite having a river, fields, gardens and woods out the back of the house !!!!
So I guess the points that I am trying to make is its almost impossible to predict where your cat will play and go . Dispite having a fantastic dream back garden both of them preferto hunt along the verge of the lane at the front where the cars are ! Secondly dspite moving to this quiet idyillic spot My Teddy got run over outside my front door 2 years ago and there are near misses every day.
I am finally coming to the conclusion that the only safe way is to fence in the garden to make a safe outdoor area which is ok if the cats grow up with it but difficult if they are used to roaming where they please. Unfortunatly I have a shared garden too ( footpath right of way) so this option isn't open to me either.
I personally think it unkind to keep cats indoors but that is because I hate to see any animal caged. Some cats seem to take to it well however especially if they have been house cats since kittens. I think cats are like humans and each have a differant personality. I think some cats will never take to being kept indoors and will always fret to get out.
Sorry not sure if my ramblings have been any help really but I suppose what I'm trying to say is moving is not always the solution