We’ve  are now totally domesticated - now 10 and 2 respectively. One: Sid Vicious (!!) is sort of as described in the OP - about aged 13.
I honestly am of the view that dogs have owners and cats have servants. So that means cats choose to come and stay with you. Feed them and they’ll hang around. Don’t free feed them though. Make sure you get into a routine and put food out at certain times each day. We tend to feed feral cats just once a day so they’re waiting for it and remain food motivated and dependent on you for food.
All ours were trapped and from feral colonies that were in breeding and extensive and causing problems. We adopted slightly different approaches with all of them. More to do with circumstances than deliberate strategies. Basically though all along the lines described by ZuZu.
I’ll tell you what we did and see if it works for you. But I think quite simply it’s a game of providing what they want - food first. Somewhere warm and comfortable next. Then companionship. If they let you stroke them and they purr then you’ll crack it.
Basil was about 7 months old when trapped brought to the farm handled from the cage trap by Susan wearing welding gloves and a welding apron and goggles! (kid you not!) Released in the feed room where he ran straight up the wall! and settled in a roof beam and there he stayed for about 3 weeks! Cat food put out on the freezer top every night and morning. He only came down to eat it when we weren’t about for about a month. Then one day he pissed off! Not seen for weeks but we continued to leave feed in the feed room. (It’s a couple of old stables and so has an open top door). Eventually he used to come to us just as you describe and if Susan sat quietly next to his feed he’d come and eat it and let her stroke him just when he was eating and he purred. Eventually he’d sit on her knee when she used to sit on the feed room step and she’d stroke him but if she made a sudden movement or anyone else came by then he’d hiss and run! Then time to put him back in a cat box and to the vet to have him neutered and vaccinated. That night it was freezing so he was permitted in our kitchen and with his cat box door open and food just outside it and a litter tray next to that. He’d used the litter tray. Food was gone the next day and so was the cat! He was behind the fridge! all day! But same the next night. Day after he was in the cat box hissing so the door was closed and he was taken back down to the yard (about 200 metres from the house). He then started to follow me about when I was doing riding lessons and then one night when I let the dogs in late, he just came in with them. Can’t get away from him now!! He’s a total pet and does most of my riding lessons with me!
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George was trapped when about 8 months old and totally assaulted! Taken straight to the vet for feline leukaemia and AIDS tests - had his ear clipped as he tested negative, so just neutered and was about to be turned to fend for himself once a farm was found when Susan went to have a coffee at the vets and came home with him! We (she!) decided as he was already in the house from the get go that we’d keep him in.
So he was shut in our bedroom and provided with food and a litter tray in the ensuite bathroom. Even though after a couple of weeks we left the door open, he spent many weeks hiding under the bed and only coming out to eat and use his tray. HIGHLY food motivated though and if you sat next to his food he’d still come out to eat and let you touch him ONLY when he ate at first. Then over time he’d come out and so we stopped feeding him upstairs and he had to take his chances in the kitchen where cats and dogs are fed. For months Susan was the only person who could pick him up or handle him. He’s still picky about who can hold him and he’s not too keen on me! I’m good enough to be his waiter and door opener and stroke him but no way will he let me pick him up! He’s all over a couple of the staff who work here and the second Sue is home he’s following her everywhere and on her knee the second she sits down.
Sid was trapped as an unneutered Tom cat about 7 years old. The size of a small terrier! We’ve never been able to handle him though he’ll come out to eat. Sue has once in 7 years handled him. We trapped him by mistake when we were trying to trap another feral unneutered that happened by! When she let him out she thought good time to give it a go so she hung on to him wedged between her knees and groomed him and removed a mass of dead coat. He stayed still and even purred after a while and she thought she might have won him over but when she finished and withdrew her (gloved) hands he hissed and determinedly struck out! Then vermoose! He’s ordinarily just seen about once a month munching on a mouse or carrying a rat out from the barn. It’s an open sided hay barn and he comes and goes and if you get close to where he is then you hear hissing from behind the hay bales and occasionally see him vanishing out at about 30 mph!
