Sorry, I don't have any carrier advice as the longest my cat has travelled is 20 minutes. Well I do have advice but it's with a rabbit....
I can only recommend what I did with Mr Mossy the rabbit when we had to move for a two hour trip (he always urinated and pooed in his carrier out of fear as he was always ill and going to the vet, so when I was a child I used this strategy when we moved). See if it sticks! You have 6 weeks so plenty of time to start a regime:
1. Bring out the cat carriers and line them out in the hall or living room, just somewhere they definitely see them and have to move past on a regular basis. Also as near their food area as possible without obstructing anyone's way. (If you don't have carriers for all cats yet I recommend you buy them ASAP so that new plastic/fabric smell gets replaced by the house smell, your smell and the cats)
2. Let them get used to the carriers. Keep the doors open or remove them if possible. Do this for 2 or 3 days.
3. Start placing food bowls in front of the carriers. Place treats. toys or additional food inside the carriers. Do this for 3-7 days pending on how your cats react.
4. Start placing each individual bowl into each individual carrier. First place at the front so they can eat without entering fully. Then move on to the middle of the carriers after 3 days. (If they have removable doors now is the time to put them back on). Finally place the bowls in the back of the carrier after a further 3-5 days.
5. Maintain this routine until you have to move. The cats will associate the carriers with food and won't be so afraid (I hope.)
6. Start picking up the cats (if you're able) and placing them in the carriers. If they go without a fuss give them a treat. Repeat until they're used to be put in without a fuss. (I recommend doing this 3 times a day or just before you feed them)
PS: perhaps it might be worth rubbing all carriers with catnip at the start to get them interested and calm around the carriers. It might also be worth installing a Feliway wherever the carriers are to get your cats to remember a calm feeling around them.
Please bear in mind I did this with a rabbit who lived in our conservatory and adapted the rules to suit a cat. So it may not work for cats and it was a long time ago that I did this. (BI: Before internet! Wow!)
I have a friend who lives in Hull. He recommended either "Kingston Veterinary Group" (They have several centres in the city), "Chants Vets" or "Vets4pets" - Those are the ones he's had the best care with. (he had a dog until recently when he passed from old age and he has 3 cats and a budgie so he'll all over the animal care regime)
EDIT: Found this on the net that may be better than my stupid "lets pretend they're rabbits" scenario.
https://www.aspca.org/pet-care/virtual- ... de-carrier" onclick="window.open(this.href);return false;