Lost but new cat found after 4 months how to integrate with the other pets

[OnceRuralNowUrbanbliss]

This is a situation I really want to get advice or ideas on.

My DD adopted a lovely friendly cat from a shelter in Nov. He got on well with our cats but was scared and aggressive towards the dog who then in turn in fear snarled and woofed at him.
Although we were keeping the new guy in he escaped 1 week after our adopting him and despite hundreds of flyers posted online and around the neighbourhood and knocking on doors we gave up hope of seeing him again.

Yesterday he was brought in to a vets as an underweight flea riddled stray who saw from his micro chip he is ours.

He's currently in the integral garage with a fan heater, comfy bed (the dogs as I felt this might help), a litter tray and plenty of food. We are going in regularly to give him a fuss.

Any ideas on how best to get the cat integrated into the household with less fear and aggression towards the dog this time?

I'm thinking perhaps let the cat into the rest of the house gradually and occasionally when the dog is shut in the garden so he can sniff around but put him back in the garage at other times, use cooked chicken for both to show they get treats when the other is around but behind different doors (glass panels will mean they see each other).

Really don't want him to scarper and get lost again.

Suspect he's got nil sense of direction hence him being a stray at a shelter when we first got him so will invest in a GPS collar I think.

Help!

I would have a good think about whey be a home with a dog is the right place for him.

I know you see lots of dogs and cats living happily together but the reality is that many don't enjoy it and become unhappy and stressed.

If your dog is also snarling at the cat, the outcome could be very unpleasant for both of them if a fight broke out - not all cats will run from dogs and a scratch in the wrong place could result in your cat being badly bitten and your dog being seriously injured.

Thanks @coffeecupsandwaxmelts that's a good point.
It is a large house with three other cats and one very small friendly dog who gets on well with his cat sibilings so would prefer to try to make this work if we can before giving up and looking for ideas on how to achieve this.

Have you got Feliway plug ins? They are supposed to help cats with anxiety.

Are there areas of the house where the dog is not allowed -ie upstairs in bedrooms? When we have a relative's dog staying with us (fairly regularly) one of our cats stays upstairs most of the time.

Do you use a crate for the dog?
I'm thinking the dog might seem less scary to the cat if the dog is in a crate.

I'm not a dog person so that might be stupid advice, I just know from reading on here mainly that a lot of dog owners do crate training or whatever it's called and it seems to me that it would help the cat settle.

I don't mean forever btw! Short periods of time together to introduce them in a less stressful way for the cat.

When we introduced our rescue cat to our dog there was instant dislike from both parties. We prevented the dog from going upstairs and the cat quickly learnt that our bedrooms were a safe haven free from canine intervention. Cat was kept indoors for 3 months (much to his dismay) and then only let out before dinner time (ie: when he was hungry) so he was eager to come home and eat. Cat slept in the kitchen with the dog from day one, but had a bed on our bay window out of our (small) dog's reach. Cat learnt to accept the dog and her grumpy ways, dog always disliked sharing me with the cat but begrudgingly learnt to coexist. They had 4 years together before our darling dog died unexpectedly and the cat definitely grieved when she left us.

Thanks all. Some good ideas. The dog is not crated and has access all areas in a fairy open plan house.

I'm swapping their beds so they get used to the smell, will use high value treats when we begin to introduce them all but will initially let the cat explore the house when the dog is out and then have controlled supervised meetings with the dog on a lead etc.