You can't add products to the car seat to make it more snug, it's not safe to do that. It comes with a newborn insert which you need to use.
I have the Joie 360 Spin GT, though I didn't use it from newborn. I meant to put DS3 into it with the newborn insert just to take some photos, but it was too full on and I never got around to it and then he was too big. I used to work in a shop selling car seats and I fitted a few newborns into them. The Joie i-Spin, GB Vaya and Maxi Cosi Mica were the best fit, but the GB Vaya is no longer made. MC Mica has a terrible fit for babies in the in-between stage from about 3-9 months because they are too big for the insert but too small to sit in the seat with no other insert, and Maxi Cosi don't make one, so I don't think it's a good option from birth, even though it has a nice fit for newborns.
So, Joie i-Spin is the best option IMO. I didn't have access to a Britax newborn insert to try, and I don't know if Cybex improved their newborn inserts. When you factor the insert costs into these seats they come to about the £270 mark anyway.
Besafe izi Turn/Twist B are even better, but they are a lot more expensive.
I don't know what seat you mean by the 360 i-size, sorry - the i-Spin is the i-size version of the Joie 360 Spin. I do think it is worth having the i-Spin over the original if you are wanting to use it from birth, because the inserts are slightly nicer/easier to use.
Newborns always look ridiculous in these huge seats. However they tend to grow quickly which is why I asked about journey from hospital and how often you'd likely go out. Attached is a series of photos of the same baby aged 2 days, 2 weeks, and 6 weeks. You can see how they do fit much better into the seat at 6 weeks old.
You do have to be fairly confident in pulling the straps over where they need to be, and a lot of people get stressed out by the Joie inserts, which have parts that you remove as the baby grows. There are a couple of good videos by Rear Facing Toddlers on Youtube about these.
You might also want to consider whether on cold or rainy days, it's going to be miserable standing at the car trying to get the baby in, as opposed to an infant carrier seat where you can spend as long as you need getting them positioned right and then tucking a blanket in over them (on top of the straps) so they are all cosy and then you just carry them to the car. They can't go into the car seat in bulky outdoor clothing, like a pramsuit - they can only wear indoor layers, like a sleepsuit and a cardigan. So if you had wrapped them up to walk to the car, you would need to unwrap them again to put them in the car. It's a bit annoying.